Harmonic Oscillator: Evaluating Ground State Probability

[glebovg]

Homework Statement

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.

Homework Equations

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

The Attempt at a Solution

How do I find m?

 

[vela]

The mass of the electron? You look it up.

 

[tiny-tim]

or you could weigh one …

if you have one on you ​

 

[glebovg]

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

 

[glebovg]

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

 

[vela]

Yes.

 

[glebovg]

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

 

[vela]

Beats me.

 

[glebovg]

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

 

[vela]

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

 

[glebovg]

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

 

[vela]

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

 

[glebovg]

It should be -0.1, right?