# Homework Help: Harmonic Oscillator

1. Mar 5, 2012

### glebovg

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

Using the normalization constant A and the value of a, evaluate the probability to find an oscillator in the ground state beyond the classical turning points ±x0. Assume an electron bound to an atomic-sized region (x0 = 0.1 nm) with an effective force constant of 1.0 eV/nm2.

2. Relevant equations

$\psi(x)=Ae^{-ax^{2}}$, where $A=(\frac{m\kappa}{\pi^{2}\hbar^{2}})^{1/8}$ and $a=\sqrt{m\kappa}/2\hbar$

3. The attempt at a solution

How do I find m?

Last edited: Mar 5, 2012
2. Mar 5, 2012

### vela

Staff Emeritus
The mass of the electron? You look it up.

3. Mar 5, 2012

### tiny-tim

or you could weigh one …

if you have one on you

4. Mar 5, 2012

### glebovg

I will try to read the question more carefully next time.

5. Mar 5, 2012

### glebovg

Am I supposed to find probabilities at both tails of the distribution?

6. Mar 5, 2012

### vela

Staff Emeritus
Yes.

7. Mar 7, 2012

### glebovg

Apparently there is an inconsistency in the question and there are two interpretations of the question. What would be the other one?

8. Mar 8, 2012

### vela

Staff Emeritus
Beats me.

9. Mar 10, 2012

### glebovg

My interpretation: find probabilities at both tails of the distribution i.e. $\int^{0}_{-\infty}\psi^{2}(x)\;dx$ and $1-\int^{0.1}_{-\infty}\psi^{2}(x)\;dx$.

10. Mar 11, 2012

### vela

Staff Emeritus
I'd say the problem is asking for one number, P(|x|>x0). The upper limit on your first integral is wrong.

11. Mar 19, 2012

### glebovg

Do you mean it is wrong according to your interpretation or it is generally wrong? Should it be 0.1?

Last edited: Mar 19, 2012
12. Mar 20, 2012

### vela

Staff Emeritus
It is generally wrong. Why would the upper limit be 0?

13. Mar 20, 2012

### glebovg

It should be -0.1, right?

Last edited: Mar 20, 2012