Quantum Mechanics and Observables

[quantumfoam]

Hi guys! I have one question! I know that in quantum mechanics, observables must be in the form of operators. However, does that mean that all observables are quantized in quantum mechanics?

 

[mpv_plate]

Hi guys! I have one question! I know that in quantum mechanics, observables must be in the form of operators. However, does that mean that all observables are quantized in quantum mechanics?

No. Operators can have continuous spectrum, so the observables may by continuous. This is the case of energy of a free particle for example.

 

[quantumfoam]

Oh okay! So if the particle was in a potential then the energy of the particle would be quantized?

 

[hilbert2]

Oh okay! So if the particle was in a potential then the energy of the particle would be quantized?

That's true for potentials that are not bounded from above (e.g. the harmonic oscillator potential). Some potentials, like that of an electron interacting with a proton, result in a set of quantized bound states with negative energy and a continuum of unbound "scattering states" with positive energy.

 

[quantumfoam]

I see.(: Thanks guys!