# A question about energy in a harmonic potential

1. Nov 21, 2004

### Physicist

Hi all,

If there is a particle in a harmonic potentail how can we find the probability that a single measurment of the system would yield to a certain energy?

How can we know which is the most probable enegy?

Thanks

2. Nov 22, 2004

### somy

I think you can find a neat answer in all elementary quantum physisics books.
See for example:
Griffiths

3. Nov 22, 2004

### Tom Mattson

Staff Emeritus
You need to know the state of the particle as a linear combination of the eigenstates &phi;n of the SHO Hamiltonian:

&psi;=&Sigma;an&phi;n

The probability of finding the partcle with energy En is the square of the modulus of the corresponding an, and the most probable energy is the eigenvalue for which this probability is largest.

4. Nov 22, 2004

### Physicist

Should I calculate the probability for all possible energies to know which one has the largest probability??

Thanks

5. Nov 22, 2004

### Tom Mattson

Staff Emeritus
If you can't tell by inspection, then you'll have to.

6. Nov 23, 2004

### Physicist

Can I say that the expectation value of the energy always has the largest probability?

&

In which cases can I tell by inspection? Can you give an example please?

Thank you very much..

7. Dec 2, 2004

### jujio77

If you want the most probably Energy or whatever just think about it this way. The probability density for some operator X, is just

psi^* X psi.

Find the maximum for this distribution.