Wave Function Sketch for Particle at Rest with Given Potential and Energy

In summary, the task is to sketch the wave function of a particle at rest, given its potential and energy. The time invariant Schroedinger equation is used to solve this problem, but the approach may vary depending on the specific conditions.
  • #1
allenh98
3
0

Homework Statement



Given the potential, and energy of a particle at rest,

Sketch the wave function

Homework Equations



The time invariant schroedinger equation

8e68702e9a85d609b6af5b46ae2e7b66.png


The Attempt at a Solution



I don't really know how to do this question

i3tanr.jpg


Basically, I am given the potential, and energy of a particle. I need to sketch the wave function of the particle given these.

Do I just integrate twice then subtract something?
 
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  • #2
Nice exercise. You done the square well potential already (or was it in the main text) ?
E is probably a constant. But what about V? If you use Vo, it looks as if you consider it constant. in some places that's OK, but not everywhere.
 

Related to Wave Function Sketch for Particle at Rest with Given Potential and Energy

1. What is a wave function?

A wave function is a mathematical description of the state of a particle or system in quantum mechanics. It describes the probability of finding the particle in a particular position or state.

2. How is the wave function related to the behavior of particles?

The wave function is related to the behavior of particles through the concept of superposition. This means that a particle can exist in multiple states or positions simultaneously, and the wave function describes the probability of each state or position.

3. Can the wave function of a particle be observed or measured?

No, the wave function itself cannot be observed or measured. However, measurements can be made on the particle, and the results can be used to determine the wave function and its properties.

4. What is the Schrödinger equation and how does it relate to the wave function?

The Schrödinger equation is a fundamental equation in quantum mechanics that describes the time evolution of a system's wave function. It relates the potential energy of a particle to its wave function and allows for the prediction of future states of the particle.

5. Can the wave function of a particle change over time?

Yes, the wave function of a particle can change over time. This is known as wave function collapse and occurs when the particle is measured or interacts with its environment. The collapse of the wave function determines the state of the particle at a given time.

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