I need just ONE analytic solution to the time-dependent Schrodinger Equation.

In summary, the speaker has been attempting to find an analytic solution for the time-dependent Schrodinger Equation in order to create a movie of the probability function. However, they have been unable to find a solution and are unsure if it is even possible without approximation. They mention trying different methods and also mention that there are analytic solutions for certain cases involving a free particle or harmonic oscillator.
  • #1
IronHamster
28
0
I have been trying to find an analytic solution to the time-dependent Schrodinger Equation. I plan to make a movie of the probability function as it changes over time, but I can't seem to find any analytic solution for the wave function.

Is it possible to solve the time-dependent Schrodinger Equation without approximation, or should I stop looking?

If it would be helpful, I can show what methods I have tried so far.
 
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  • #2
There are analytic solutions for either a free particle or for a harmonic oscillator with a wave function of the form exp[-a(t)x^2 - b(t)x], where a(t) and b(t) are particular complex functions of time.
 

1. What is the time-dependent Schrodinger Equation?

The time-dependent Schrodinger Equation is a fundamental equation in quantum mechanics that describes the evolution of a quantum system over time.

2. Why is it important to find an analytic solution to the time-dependent Schrodinger Equation?

Finding an analytic solution to the time-dependent Schrodinger Equation allows us to accurately predict the behavior of quantum systems and understand the underlying physical principles governing them.

3. Is it possible to find just one analytic solution to the time-dependent Schrodinger Equation?

Yes, it is possible to find one analytic solution to the time-dependent Schrodinger Equation. However, this solution may not be applicable to all quantum systems and may only provide insight into a specific scenario.

4. What are the challenges in finding an analytic solution to the time-dependent Schrodinger Equation?

The time-dependent Schrodinger Equation is a highly complex differential equation, making it difficult to find an exact analytic solution. Additionally, the solution may involve complex mathematical operations and may not be easily interpreted.

5. Are there any alternative methods for solving the time-dependent Schrodinger Equation?

Yes, there are alternative methods such as numerical methods and approximation techniques that can be used to solve the time-dependent Schrodinger Equation. These methods may not provide an exact analytic solution, but can still give valuable insights into the behavior of quantum systems.

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