Wave function in infinite square well, with potential step

In summary, the conversation discusses finding the wave function of a particle trapped in an infinite square well with varying potential energy. The 1-D time independent Schrodinger equation is used and the correct wavefunctions are found for different energies (E>U0, E<U0, and E=U0). The process of joining these wavefunctions together is discussed, with the suggestion to use boundary conditions to determine the integration constants.
  • #1
slasakai
16
0

Homework Statement


A Particle energy A trapped in infinite square well. U(x)=0 for 0<x<L and U(x)=U0 for L<x<2L. find the wave function of the particle when A) E>U0 B) E<U0 C) E=U0.

Homework Equations


1-D time independent Schrodinger equation.



The Attempt at a Solution



I have the correct wavefunctions for the particle from 0<x<L and L<x<2L ,(have checked solutions) however I don't understand how to write join them together into one function.

any help would be appreciated, I am new to this subject so please go easy on me haha.

thanks in advance,

S.
 
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  • #2
When you say "I have the correct wavefunctions" you mean general solutions with integration constants ? Those can be found by applying the proper boundary conditions: that way you "join" the wavefunctions . So under 2. you should list some of these conditions.
 

1. What is the wave function in an infinite square well?

The wave function in an infinite square well is a mathematical function that describes the probability of finding a particle in a particular position within the well. It is a solution to the Schrödinger equation and is represented by a sine or cosine function.

2. How does the potential step affect the wave function?

The potential step creates a sudden change in potential energy within the infinite square well. This causes the wave function to split into two separate functions, with one representing the particle before the step and the other representing the particle after the step. The amplitude of the wave function may also change depending on the height of the step.

3. What is the role of boundary conditions in the wave function of an infinite square well with a potential step?

Boundary conditions play a crucial role in determining the form of the wave function in an infinite square well with a potential step. These conditions ensure that the wave function is continuous and differentiable at the boundaries of the well, and that it approaches zero at infinity.

4. How does the energy of the particle change when it encounters a potential step in an infinite square well?

The energy of the particle remains constant as it encounters a potential step in an infinite square well. However, the wave function may change in amplitude and phase, which can affect the probability of finding the particle in different positions within the well.

5. Can the wave function be used to determine the exact position and momentum of a particle in an infinite square well with a potential step?

No, the wave function only describes the probability of finding a particle in a specific position within the well. The position and momentum of a particle cannot be simultaneously determined with certainty according to the Heisenberg uncertainty principle. However, the wave function can provide information about the average position and momentum of the particle.

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