How Do You Find the Time Evolution of a Wave Function in Quantum Mechanics?

In summary, the conversation discusses finding the wave function at a given time t, with the speaker expressing confusion and lack of examples in their book. They are then asked about the time evolution of a wavefunction and if they have been introduced to the time evolution operator. Finally, they are given a hint to use the time dependent Schrodinger equation to find the change in the wave function over time.
  • #1
mathlete
151
0
I'm given the value of a normalized wave function at t=0 (see attachment) and I'm asked to find the wave function at some time t. I have no idea where to even begin, the book has zero examples of anything and I'm just stuck :confused:
 

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  • #2
What does your book have to say about the time evolution of a wavefunction? More specifically, have you been told what the time evolution operator is?
 
  • #3
mathlete,

I can't see yout attachment so I don't know what level you're at, therefore I'm going to give a fairly basic approach. If I have an exact energy state [tex] \psi_E(x) [/tex] that satisfies the time independent Schrodinger equation [tex] H \psi_E = -\frac{\hbar^2}{2m} \frac{d^2\psi_E}{dx^2} + V \psi_E= E \psi_E, [/tex] then how does [tex] \psi_E [/tex] change in time? Hint: use the time dependent Schrodinger equation.
 

1. What is the Schrodinger equation?

The Schrodinger equation is a fundamental equation in quantum mechanics that describes the evolution of a quantum state over time. It was developed by Austrian physicist Erwin Schrodinger in 1926.

2. Why is the Schrodinger equation important?

The Schrodinger equation is important because it allows us to make predictions about the behavior of quantum systems, such as atoms and subatomic particles. It has been proven to accurately describe many physical phenomena and is the foundation of modern quantum mechanics.

3. How do you solve the Schrodinger equation?

The Schrodinger equation can be solved using mathematical techniques such as separation of variables, perturbation theory, and numerical methods. The solution gives the probability amplitude for finding a particle at a specific location in space and time.

4. What are some applications of the Schrodinger equation?

The Schrodinger equation has numerous applications in physics, chemistry, and engineering. It is used to study the behavior of atoms, molecules, and other quantum systems. It is also used in the development of technologies such as lasers, transistors, and superconductors.

5. Is the Schrodinger equation limited to small-scale systems?

No, the Schrodinger equation can be applied to systems of any size. While it is often used to describe the behavior of particles at the atomic and subatomic level, it can also be used to study larger systems such as molecules and even macroscopic objects. However, for larger systems, the equations become much more complex and difficult to solve.

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