# Depth of a finite square potential problem

1. Jan 31, 2012

### aglo6509

1. The problem statement, all variables and given/known data

Consider a finite square-well potential well of width 3.00x10-15 m that contains a particle of mass 1.88 GeV/c2. How deep does the well need to be to contain three energy levels?

2. Relevant equations

3. The attempt at a solution

I think I have to use the formula for penetration density:

δx=(hbar)/(sqrt(2m(V0-E)))
V0=0 because the particle is inside the well.

Would I use:

En=(n-1/2)(hbar)ω to find the energy of three levels?

Then would I plug this formula back into the penetration density formula to find the penetration density?

Thank you.

2. Feb 1, 2012

### Simon Bridge

You know how the bound-state energy levels are calculated right?

The third bound state will be the second symmetric state.
So why not use the standard parameterization?

Plot $y=v\tan v$ - the value of v where the second curve hits the v axis is the minimum value of $u_0$ to contain 3 states, and:
$$u_0^2 = \frac{mL^2V_0}{2\hbar}$$

Don't think this counts as introductory physics though.

3. Oct 30, 2012

### markovcy

I believe you need to approximate the energy as if it were in an infinite well:

E=n2(hbar2)(π2)/(2mL2)

with n=3

4. Oct 31, 2012

### Simon Bridge

@aglo6509: how did you get on? As you see, you are attracting attention 8 months later ;)
@markovcy: welcome to PF; it is nice of you to start out by answering questions.
Under "get posts" at the top, there is an option to look for recent posts that have yet to be replied to - just saying.

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