Energy of free particle not quantized?

1. Apr 18, 2012

Aziza

what does it mean that the energy of a free particle is not quantized, but continuous just like in classical physics? I thought energy is always quantized??

2. Apr 18, 2012

Khashishi

Energy is not quantized for a free particle. The particle can have whatever kinetic energy.

3. Apr 18, 2012

HallsofIvy

Staff Emeritus
A particle constrained to a finite interval has quantized energy. A "free particle", that can move any where in space, has continuous energy. Mathematically, that is because the eigenvalues on a finite interval (where you can use a Fourier series) are discrete while the eigenvalues on an infinite interval (where you can use a Fourier integral) are continuous.

4. Apr 18, 2012

tannerbk

Energy is not quantized in this case because the free particle does not represent a possible physical state. Rather, it is a useful description in the study of one dimensional scattering. None of the eigenfunctions of the moment operator live in Hilbert Space, thus they do not represent a physically realizable state. However, you can recover Dirac Orthonormality and the eigenfunctions are complete, so the free particle is very useful when applied to other problems.

5. Apr 19, 2012

haruspex

What's always quantised is action; energy * time, momentum * position,...
Energy becomes quantised in consequence when time is constrained to discrete values, such as the period of a photon, or of an electron in orbit. Free electrons have no such time constraint.