In quantum mechanics, it is usually said that energy of the bound (constrained) systems such as particle in a box (infinite potential well) is quantized. It confuses me exactly what type of energy is this? Is it kinetic energy, potential energy or total energy of the particle?
It is also said that particle in a box has some positive non-zero energy even in the ground state. So if this is the kinetic energy then does that implies that particle moves around in the box even in the lowest energy state?
Sometimes in physics the "energy" is used to denote the total energy while other times it is used as a shorthand for "kinetic energy". In most cases it can be derived from the context on which energy is meant but other times it is confusing for me when not explicitly stated.
Best Answer
In the ground state the particle moves with non-zero kinetic energy. In your case this kinetic energy is certain, it is quantized, but the momentum $\vec{P}$ is uncertain - its mean value is zero with non-zero mean square $\langle P^2\rangle >0$. The particle position is also uncertain and the wave function squared gives its probability distribution. The particle is always observed as a particle, but the probability of finding it here or there is determined with the wave function.