Quantum Mechanics Problem

In summary, the homework problem involves analyzing the potential V(x) = alpha*delta(x) -a<x<a and V(x) = infinity for |x|>a and finding the allowed energies by examining the even and odd solutions separately. The even solutions are defined as \psi(x) = A*cos(kx) for 0<x<a and \psi(-x) for -a<x<0. The problem is to determine if these solutions exist, and if so, the correct form for them. The concept of even and odd solutions refers to solutions that are even or odd under coordinate inversion. The individual attempting the problem is unsure if their approach is correct and seeks clarification.
  • #1

G01

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Homework Statement


Consider the potential:

[tex] V(x) = \alpha\delta(x)[/tex] -a<x<a
[tex] V(x) = \infinity[/tex] |x|>a


Analyze the even and odd solutions separately, and find the allowed energies.

Homework Equations





The Attempt at a Solution



So far, I looked at the even solutions:

[tex] \psi(x)=A\cos(kx)[/tex] 0<x<a
[tex]\psi(-x)[/tex] -a<x<0

With this solution, Acoskx must equal zero at the delta barrier correct?
Since the only way this could happen is for A=0, am I to assume the even solutions don't exist?

Am I going about this correctly? Thanks for any help you can offer.
 
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  • #2
I think I may be confused on what they mean by "the even and odd solutions."
 
Last edited:
  • #3
Solutions which are odd and even under coordinate inversion...
 
  • #4
Ok I think I get that much, did I at least start this problem the correct way? Like, do I have the correct form of the even solutions?
 

1. What is quantum mechanics?

Quantum mechanics is a branch of physics that deals with the behavior of matter and energy at a very small scale, such as atoms and subatomic particles.

2. What is a quantum mechanics problem?

A quantum mechanics problem is a mathematical or conceptual challenge that arises from the principles of quantum mechanics and requires its methods and theories to be solved.

3. Why is quantum mechanics important?

Quantum mechanics is important because it helps us understand the behavior of matter and energy at the smallest scales, which is crucial for many areas of science and technology, such as electronics, chemistry, and materials science.

4. What are the key principles of quantum mechanics?

The key principles of quantum mechanics are superposition, entanglement, and uncertainty. Superposition refers to the ability of particles to exist in multiple states at the same time. Entanglement describes the correlation between particles that can exist even when they are separated. Uncertainty refers to the inherent unpredictability of particles at the quantum level.

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Quantum mechanics has many practical applications, such as in the development of new technologies like transistors and lasers, cryptography, and quantum computing. It also helps us understand and predict the behavior of materials and particles at the smallest scales, which is crucial for many industries and fields of research.

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