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# Understand the Fourier Transform : Start From Quantum Mechanics

The Fourier transform has a million applications across all sorts of fields in science and math. But one of the very deepest arises in quantum mechanics, where it provides a map between two parallel descriptions of a quantum particle: one in terms of the position space wavefunction, and a dual description in terms of the momentum space wavefunction. Understanding this connection is also one of the best ways of learning what the Fourier transform really means.

We'll start by thinking about the quantum mechanics of a particle on a circle, which requires that the wavefunction be periodic. That lets us expand it in a Fourier series---a superposition of many sine and cosine functions, or equivalently complex exponential functions. We'll see that these individual Fourier waves are the eigenfunctions of the quantum momentum operator, and the corresponding eigenvalues are the numbers we can get when we go to measure the momentum of the particle. The coefficients of the Fourier series tell us the probabilities of which value we'll get.

Then, by taking the limit where the radius of this circular space goes to infinity, we'll return to the quantum mechanics of a particle on an infinite line. And what we'll discover is that the full-fledged Fourier transform emerges directly from the Fourier series in this limit, and that gives us a powerful intuition for understanding what the Fourier transform means. We'll look at an example that shows that when the position space wavefunction is a narrow spike, so that we have a good idea of where the particle is in space, the momentum space wavefunction will be spread out across a huge range. By knowing the position of the particle precisely, we don't have a clue what the momentum will be, and vice-versa! This is the Heisenberg uncertainty principle in action.

0:00 Introduction
2:56 The Fourier series
16:08 The Fourier transform
25:37 An example

Develop a deep understanding of the Fourier transform by appreciating the critical role it plays in quantum mechanics! Get the notes for free here: https://courses.physicswithelliot.com/notes-sign-up

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## Google's TPU's being primed for the Quantum Jump

The liquid-cooled Tensor Processing Units, built to slot into server racks, can deliver up to 100 petaflops of compute.

The liquid-cooled Tensor Processing Units, built to slot into server racks, can deliver up to 100 petaflops of compute.

As the world is gearing towards more automation and AI, the need for quantum computing has also grown exponentially. Quantum computing lies at the intersection of quantum physics and high-end computer technology, and in more than one way, hold the key to our AI-driven future.

Quantum computing requires state-of-the-art tools to perform high-end computing. This is where TPUs come in handy. TPUs or Tensor Processing Units are custom-built ASICs (Application Specific Integrated Circuits) to execute machine learning tasks efficiently. TPUs are specific hardware developed by Google for neural network machine learning, specially customised to Google’s Machine Learning software, Tensorflow.

The liquid-cooled Tensor Processing units, built to slot into server racks, can deliver up to 100 petaflops of compute. It powers Google products like Google Search, Gmail, Google Photos and Google Cloud AI APIs.

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## Quantum Physics Full Course | Quantum Mechanics Course

Quantum physics also known as Quantum mechanics is a fundamental theory in physics that provides a description of the physical properties of nature at the scale of atoms and subatomic particles. It is the foundation of all #quantum #physics including quantum chemistry, quantum field theory, quantum technology, and quantum information science.

In this course you will learn about Quantum #mechanics from the beginning to the end. The following topics of Quantum mechanics have been discussed in this course:

⌨️  (0:00:00) Introduction to quantum mechanics
⌨️  (0:16:23) The domain of quantum mechanics
⌨️  (0:24:18) Key concepts of quantum mechanics
⌨️  (0:34:04) A review of complex numbers for QM
⌨️  (0:48:12) Examples of complex numbers
⌨️  (1:01:47) Probability in quantum mechanics
⌨️  (1:12:17) Variance of probability distribution
⌨️  (1:26:16) Normalization of wave function
⌨️  (1:51:47) Position, velocity and momentum from the wave function
⌨️  (2:10:59) Introduction to the uncertainty principle
⌨️  (2:24:32) Key concepts of QM - revisited
⌨️  (2:37:45) Separation of variables and Schrodinger equation
⌨️  (3:09:55) Stationary solutions to the Schrodinger equation
⌨️  (3:15:47) Superposition of stationary states
⌨️  (3:25:37) Potential function in the Schrodinger equation
⌨️  (3:48:10) Infinite square well (particle in a box)
⌨️  (4:00:58) Infinite square well states, orthogonality - Fourier series
⌨️  (4:08:07) Infinite square well example - computation and simulation
⌨️  (4:39:27) Quantum harmonic oscillators via ladder operators
⌨️  (5:16:48) Quantum harmonic oscillators via power series
⌨️  (5:28:32) Free particles and Schrodinger equation
⌨️  (5:34:37) Free particles wave packets and stationary states
⌨️  (6:10:33) Free particle wave packet example
⌨️  (6:13:43) The Dirac delta function
⌨️  (6:20:49) Boundary conditions in the time independent Schrodinger equation
⌨️  (6:24:39) The bound state solution to the delta function potential TISE
⌨️  (6:43:29) Scattering delta function potential
⌨️  (6:55:49) Finite square well scattering states
⌨️  (7:07:39) Linear algebra introduction for quantum mechanics
⌨️  (7:10:34) Linear transformation
⌨️  (7:13:04) Mathematical formalism is Quantum mechanics
⌨️  (7:37:52) Hermitian operator  eigen-stuff
⌨️  (8:01:23) Statistics in formalized quantum mechanics
⌨️  (8:24:26) Generalized uncertainty principle
⌨️  (8:54:36) Energy time uncertainty
⌨️  (9:16:33) Schrodinger equation in 3d
⌨️  (9:19:56) Hydrogen spectrum
⌨️  (9:31:14) Angular momentum operator algebra
⌨️  (9:57:17) Angular momentum eigen function
⌨️  (10:18:08) Spin in quantum mechanics
⌨️  (10:22:23) Two particles system
⌨️  (10:58:03) Free electrons in conductors
⌨️  (11:09:23) Band structure of energy levels in solids

#quantum #developer #programming

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## How to start an electric scooter facility/fleet in a university campus/IT park

Are you leading an organization that has a large campus, e.g., a large university? You are probably thinking of introducing an electric scooter/bicycle fleet on the campus, and why wouldn’t you?

Introducing micro-mobility in your campus with the help of such a fleet would help the people on the campus significantly. People would save money since they don’t need to use a car for a short distance. Your campus will see a drastic reduction in congestion, moreover, its carbon footprint will reduce.

Micro-mobility is relatively new though and you would need help. You would need to select an appropriate fleet of vehicles. The people on your campus would need to find electric scooters or electric bikes for commuting, and you need to provide a solution for this.

To be more specific, you need a short-term electric bike rental app. With such an app, you will be able to easily offer micro-mobility to the people on the campus. We at Devathon have built Autorent exactly for this.

What does Autorent do and how can it help you? How does it enable you to introduce micro-mobility on your campus? We explain these in this article, however, we will touch upon a few basics first.

## Micro-mobility: What it is

You are probably thinking about micro-mobility relatively recently, aren’t you? A few relevant insights about it could help you to better appreciate its importance.

Micro-mobility is a new trend in transportation, and it uses vehicles that are considerably smaller than cars. Electric scooters (e-scooters) and electric bikes (e-bikes) are the most popular forms of micro-mobility, however, there are also e-unicycles and e-skateboards.

You might have already seen e-scooters, which are kick scooters that come with a motor. Thanks to its motor, an e-scooter can achieve a speed of up to 20 km/h. On the other hand, e-bikes are popular in China and Japan, and they come with a motor, and you can reach a speed of 40 km/h.

You obviously can’t use these vehicles for very long commutes, however, what if you need to travel a short distance? Even if you have a reasonable public transport facility in the city, it might not cover the route you need to take. Take the example of a large university campus. Such a campus is often at a considerable distance from the central business district of the city where it’s located. While public transport facilities may serve the central business district, they wouldn’t serve this large campus. Currently, many people drive their cars even for short distances.

As you know, that brings its own set of challenges. Vehicular traffic adds significantly to pollution, moreover, finding a parking spot can be hard in crowded urban districts.

Well, you can reduce your carbon footprint if you use an electric car. However, electric cars are still new, and many countries are still building the necessary infrastructure for them. Your large campus might not have the necessary infrastructure for them either. Presently, electric cars don’t represent a viable option in most geographies.

As a result, you need to buy and maintain a car even if your commute is short. In addition to dealing with parking problems, you need to spend significantly on your car.

All of these factors have combined to make people sit up and think seriously about cars. Many people are now seriously considering whether a car is really the best option even if they have to commute only a short distance.

This is where micro-mobility enters the picture. When you commute a short distance regularly, e-scooters or e-bikes are viable options. You limit your carbon footprints and you cut costs!

Businesses have seen this shift in thinking, and e-scooter companies like Lime and Bird have entered this field in a big way. They let you rent e-scooters by the minute. On the other hand, start-ups like Jump and Lyft have entered the e-bike market.

Think of your campus now! The people there might need to travel short distances within the campus, and e-scooters can really help them.

## How micro-mobility can benefit you

What advantages can you get from micro-mobility? Let’s take a deeper look into this question.

Micro-mobility can offer several advantages to the people on your campus, e.g.:

• Affordability: Shared e-scooters are cheaper than other mass transportation options. Remember that the people on your campus will use them on a shared basis, and they will pay for their short commutes only. Well, depending on your operating model, you might even let them use shared e-scooters or e-bikes for free!
• Convenience: Users don’t need to worry about finding parking spots for shared e-scooters since these are small. They can easily travel from point A to point B on your campus with the help of these e-scooters.
• Environmentally sustainable: Shared e-scooters reduce the carbon footprint, moreover, they decongest the roads. Statistics from the pilot programs in cities like Portland and Denver showimpressive gains around this key aspect.
• Safety: This one’s obvious, isn’t it? When people on your campus use small e-scooters or e-bikes instead of cars, the problem of overspeeding will disappear. you will see fewer accidents.

#android app #autorent #ios app #mobile app development #app like bird #app like bounce #app like lime #autorent #bird scooter business model #bird scooter rental #bird scooter rental cost #bird scooter rental price #clone app like bird #clone app like bounce #clone app like lime #electric rental scooters #electric scooter company #electric scooter rental business #how do you start a moped #how to start a moped #how to start a scooter rental business #how to start an electric company #how to start electric scooterrental business #lime scooter business model #scooter franchise #scooter rental business #scooter rental business for sale #scooter rental business insurance #scooters franchise cost #white label app like bird #white label app like bounce #white label app like lime

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## The essential feature that are integrated into Uber For Mechanics

The on demand mechanic app has driven to fast change in this digital age offering solution from the comfort of home. The success of the mechanic app was because of the simple accessibility for users. listed below are the break up the workflow. If you are planning on developing an on demand mechanics service app, here are a few elements that you need to consider.

Secure login- Users can simply login via OTP that is sent to their register mobile number.Social login is very easy so much so it takes under a second to create a profile.

Search for mechanic- With the history of the mechanic and the service score the mechanic profile is listed when search.

Book and schedule repair- The user can book the service to the check-out and schedule the pick up at their feasible time.

**Cancellation- **By providing with valid reason the user can either reschedule or cancel the booking.

Payment and Review- The payment can be made through digital wallet or national payment options and once the service is completed and after thorough inspection of the customer can rate and review the service.

Conclusion:

People prefer to get things done most efficiently, and on-demand service apps have provided the perfect solution. They need not have to step outside their doorsteps and can get essential services to their home with a few taps and swipes on their smartphone. They have been a boon to service providers as they are able to boost their overall revenue conveniently. With every step subsequent to booking an uber for mechanic there are features that helps users experience more efficiently.

#uber for mechanics #uber for mechanics app #uber for mechanic service #on demand mechanics service app #on demand mechanic app

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## Invest and encash from an profitable online venture with Uber For Mechanics

Owning a vehicle is a boon and sorrow with the growing/escalating city conditions. Every vehicle owner is faced with some trouble when having a vehicle. The real problem arises when the owners require quick and reliable assistance.

Now the rise of uber apps for different services have captivated many entrepreneurs and startups to come forward and launch a business in many on-demand sectors. Uber for mechanics is one such a domain offering great opportunities for newbies to enter and secure a place in the growing market.

The new players in town would need a tool to enter in the on-demand market. Clone apps like Uber For Mechanics provide the appropriate digital platform for them. These clone apps are significantly cheaper than building a new app from scratch. With endless customizations, the app can be reframed to fit all the essential business ideas that align with the app’s revenue generation.

These On-demand Mechanics App Development app should provide the users with their needs by performing every requested task effortlessly. To function at a superior state, the app must be integrated with the best and mindful features. It is essential not to crowd the app with all the features since it will bring down the user’s usability.

Let’s take a look at the features that play an important role.

Collective features that are helping in running a three-point business

Multi-payment portals
The customers are provided with all the national payment gateways for an easy and secure transaction.
Live-tracking
With the feature, the customer and the admin panel can track the location of the service provider.
Mechanic profile
The customers, when booking a required service, can view the profile and history of the mechanic.
Intelligent dispatch
As soon as the customer books a service, the service provider is notified, and the serviceman receives an alert for immediate dispatch to the customer location.

#uber for mechanics #uber for mechanics app #uber for mechanic service #on demand mechanics service app #on demand mechanic app