A question about energy in a harmonic potential

[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

[somy]

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

[Tom Mattson]

You need to know the state of the particle as a linear combination of the eigenstates φn of the SHO Hamiltonian:

ψ=Σanφn

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.

[Physicist]

and the most probable energy is the eigenvalue for which this probability is largest.

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

Thanks

[Tom Mattson]

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


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

[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..

[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.