QM: Potential Energy & Particle Free Fall

[LagrangeEuler]

In classical mechanics is defined potential and kinetical energy for particular particle. For example, in case of free fall potential energy of the particle is $mgh$ and kinetic energy is $\frac{m\upsilon^2}{2}$. In QM there isn't potential of the particle, but potential of part of the space. For example particle could be in the space part where whole energy of the particle is less then potential. Could you explain me this? I'm really confused with this.

 

[mfb]

There is no such difference between classical mechanics and QM. The potential for a specific particle is a function of space both in quantum mechanics and classical mechanics. The total energy is a property of the particle both in quantum mechanics and classical mechanics.

or example particle could be in the space part where whole energy of the particle is less then potential.

That is a difference, right. In quantum mechanics, the particle can be at locations forbidden for a classical particle (as it does not have enough energy).

 

[andrien]

In case one can get a matrix element and take it's non relativistic form,fourier transform of it gives a potential.