When is energy quantized in a one dimensional potential.

[ItsFootballNo]

Homework Statement

Consider a non relativistic particle moving in a 1D potential V(x). Do you consider the energy of a particle moving in this potential to be quantized?

Homework Equations

V(x)=A exp{alpha^2 x^2}

The Attempt at a Solution

I was a bit confused as I thought energy was always quantized. My other thought was whether it is merely quantized in classically allowed zones and not in classically forbidden regions. In this case, the classically forbidden zones would be when |x| is greater than sqrt{2E/mw^2} if we approximate the potential as a harmonic oscillator.

Thanks for any help and apologies for any stupid errors I might have made. :S

*I was also unsure whether this would come under advanced physics or intro physics and if I have posted in the wrong forum, I apologise.

 

[nilesh_pat]

Yes, the energy of a particle moving in a 1D potential V(x) is quantized. This is because the total energy of the particle, E, is equal to the sum of the kinetic energy, T, and potential energy, U: E=T+U. The kinetic energy of the particle is quantized according to the de Broglie equation, E=hf, where h is Planck's constant and f is the frequency of the particle's motion. The potential energy is also quantized, because it is a function of the position of the particle. Therefore, the total energy of the particle is quantized.