# Time-dependant Schrödinger Equation Help.

• castusalbuscor
In summary, the conversation discusses a project due in mid March that involves writing a computer program to demonstrate the reflection of a wave packet off a barrier. The individual recalls a similar project from a previous class but expresses confusion about the concepts. They mention borrowing a book from a professor and inquire about helpful equations and how to begin the project. A suggested numerical method, "split-operator FFT," is mentioned.
castusalbuscor
I have a project to work on that's due by mid March.

I would need to write a computer program, to show how a wave packet reflect off a barrier? How much of the wave reflects off a wall of finite height and thickness, and how much tunnels through?

I remember doing something similar in my first Quantum Mechanics class last term, but we only covered the Time-Independent Schrödinger equation, and I remember that the concepts got me slightly confused.

Unfortunately I do not own the Quantum Mechanics book, I borrowed one from one of the professors in the department.

What equations would be of great use to me? And how would I go about to actually start on the project?

Look up "split-operator FFT", it is a numerical method which should work well for this problem.

First of all, I would recommend reviewing the Time-Independent Schrödinger equation and its concepts before delving into the Time-Dependent Schrödinger equation. It is important to have a solid understanding of the basics before moving on to more complex equations.

For your project, you will need to write a computer program to simulate the behavior of a wave packet reflecting off a barrier. This will involve using the Time-Dependent Schrödinger equation, which describes the evolution of a quantum system over time.

To start, you will need to define the initial conditions of your wave packet, such as its position, momentum, and energy. Then, using the Time-Dependent Schrödinger equation, you can calculate how the wave packet will evolve over time.

As for the equations that would be useful for your project, you will need to use the Time-Dependent Schrödinger equation, as well as other equations from Quantum Mechanics such as the wave function, Hamiltonian operator, and probability density function. It would also be helpful to review concepts such as wave-particle duality, superposition, and tunneling.

To actually start on the project, I would suggest breaking it down into smaller tasks and setting a timeline for each task. This could include researching and understanding the necessary equations, designing and writing the computer program, and analyzing and interpreting the results.

Additionally, it may be helpful to consult with your professor or other experts in the field for guidance and clarification on any confusing concepts. Good luck with your project!

## 1. What is the Time-dependant Schrödinger Equation?

The Time-dependant Schrödinger Equation is a mathematical equation in quantum mechanics that describes how the wave function of a physical system evolves over time.

## 2. What is the significance of the Time-dependant Schrödinger Equation in quantum mechanics?

The Time-dependant Schrödinger Equation is a fundamental equation in quantum mechanics that allows us to predict the behavior of quantum systems over time. It is essential for understanding the behavior of particles at the microscopic level.

## 3. How is the Time-dependant Schrödinger Equation derived?

The Time-dependant Schrödinger Equation is derived from the more general Schrödinger Equation, which is a fundamental equation in quantum mechanics. It is obtained by adding a time-dependent term to the Schrödinger Equation, which accounts for the time evolution of the wave function.

## 4. What are the key assumptions of the Time-dependant Schrödinger Equation?

The Time-dependant Schrödinger Equation is based on two key assumptions: the wave-particle duality of matter and the principle of superposition. These assumptions allow us to describe the behavior of particles as waves and to model the behavior of complex systems as a combination of simpler systems.

## 5. How is the Time-dependant Schrödinger Equation solved?

The Time-dependant Schrödinger Equation is a partial differential equation, which means that it requires advanced mathematical techniques to solve. Some common methods for solving the equation include separation of variables, perturbation theory, and numerical methods such as the finite difference method.

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