Can a quantum particle confined in a one-dimensional box in the n = 1 state release (give off) energy.

Answer 1

The simple answer is YES.

A particle in a 1-dimensional box is a fundamental quantum mechanical approximation describing the translational motion of a single particle confined inside an infinitely deep well from which it cannot escape.

The lowest possible energy of a particle is NOT zero. This is called the zero-point energy and means the particle can never be at rest because it always has some kinetic energy.