Schrödinger Equation: Solving for Energy in a Semi-Infinite Square Well"

In summary, the conversation discusses solving a problem involving a semi-infinite square well and the Schrödinger equation. The individual is having trouble finding the value of m and solving for the other variables. They mention using the equation E= K^2= 2mE/h^2 and rearranging it to (K^2 • h^2)/(2m) =E. They also mention that the first derivatives must be equal at X=L and provide equations for this condition. The individual is unsure if they are on the right track and may need to post in a more advanced physics forum for assistance.
  • #1
Ashley1nOnly
132
3

Homework Statement


I have an attachment

Homework Equations


Schrödinger equation

The Attempt at a Solution


The issues I am having is how to start this one. This is not a infinite square well but a semi-infinite square well.
I know that energy= K^2= 2mE/h^2
Where h is planks constant 6.626 X 10^-34 J•s
So rearranging (K^2 • h^2)/(2m) =E
How do I find my m and solve the other ones

At X=L
The first derivatives must be equal at X=L
Asin(kL)=Ce^(-aL)
KAcos(kL)=-aCe^(-aL)

Am I going in the right direction
 
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  • #2
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  • #3
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  • #4
I think this belongs in the advanced physics forum.
 

What is the Schrödinger equation?

The Schrödinger equation is a fundamental equation in quantum mechanics that describes the evolution of a quantum system over time. It is used to calculate the probability of finding a particle in a particular state at a given time.

What is a semi-infinite square well?

A semi-infinite square well is a potential energy function that is used to model certain quantum systems. It consists of a square well potential that extends infinitely in one direction and is finite in the other direction.

How is the Schrödinger equation used to solve for energy in a semi-infinite square well?

The Schrödinger equation is solved by applying boundary conditions at the edges of the square well. These boundary conditions determine the allowed energy levels for the system.

What are the key assumptions made when solving for energy in a semi-infinite square well?

The key assumptions made when solving for energy in a semi-infinite square well include: the potential energy function is constant inside the well, the potential energy outside the well is infinite, and the potential energy is zero at the edges of the well.

What are the implications of solving for energy in a semi-infinite square well?

Solving for energy in a semi-infinite square well allows us to understand the energy levels and probability of finding a particle in a given state within a specific quantum system. It also provides insights into the behavior of quantum systems and can be used to predict and explain experimental results.

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