Analytical solution for bound state energies of infinite well

Solving the equation E^1/2 tan(2ma^2E/4hbar)^1/2 = (V0-E)^1/2 can give one curve for the RHS and several curves for the LHS, with the intersection points corresponding to the solutions for n. It is possible to solve this equation using Matlab or Mathematica. However, more information is needed to accurately solve the equation, such as the specific potential being used.
  • #1
Bob007
1
0
Hi there
I am trying to find bound state energies assuming infinite potential. I have been told it can be done by analytically solving Right Hand Side and Left Hand Side of an equation such as:
E^1/2 tan(2ma^2E/4hbar)^1/2 = (V0-E)^1/2
If solved properly, it should give one curve (RHS), crossed by several LHS curves. Intersection points are the answers I am looking for. Each intersection corresponds to one n. I am wondering if it can be done by Matlab or Mathematica? Sorry if it is too basic :)
Thanks
 
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  • #2
Bob007 said:
assuming infinite potential
That doesn't specify what the potential is! Assuming infinite potential where?

Also you can't solve RHS and LHS of an equation, you solve the equation itself!

Your explanations are inadequate and unclear!
 
  • #3
Bob007 said:
I am trying to find bound state energies assuming infinite potential.

Do you mean the finite or the infinite potential well?
 

What is an analytical solution for bound state energies of infinite well?

An analytical solution for bound state energies of infinite well is a mathematical solution that can be solved using equations and formulas without the need for numerical methods or approximations. It provides a precise and exact solution for the energy levels of a particle confined in an infinite well potential.

What is an infinite well potential?

An infinite well potential is a theoretical model in quantum mechanics that describes a particle confined within a box with infinitely high potential walls. This means that the particle cannot escape from the box and its energy is quantized, meaning it can only have certain discrete energy levels.

How is the analytical solution for bound state energies of infinite well derived?

The analytical solution for bound state energies of infinite well is derived by solving the Schrödinger equation for the particle in the infinite well potential. This involves using boundary conditions and applying mathematical techniques such as separation of variables and integration to find the energy eigenvalues and corresponding wavefunctions.

What are the advantages of using an analytical solution for bound state energies of infinite well?

Analytical solutions provide a more accurate and precise solution compared to numerical methods or approximations. They also allow for a deeper understanding of the physical principles involved and can be used to make predictions for other systems with similar properties.

What are the limitations of the analytical solution for bound state energies of infinite well?

The analytical solution for bound state energies of infinite well is only applicable to idealized systems with infinitely high potential walls. In real systems, there may be imperfections or variations in the potential well that can affect the accuracy of the solution. It also does not account for other factors such as interactions with other particles or external fields.

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