A quantum mechanical system ( particle , atom , molecule , etc.) is in an energy state of its own if its energy has a well-defined value. In the case of bound systems , the energy values possible for this do not form a continuous spectrum , but a discrete , i.e. That is, they can only assume certain values with also certain intervals.
Energy eigenstates are stationary , i.e. That is, the measurable properties of the system do not change as long as it remains in this state. Transitions to other natural energy states of the system with other energy only take place when the corresponding energy difference is supplied or released in the form of an interaction with a second system. If at least one of the two systems has a discrete spectrum, only the energies of a suitable size can be exchanged, the quanta . Max Planck was the first to consider this phenomenon in 1900, marking the beginning of quantum physics .
Due to the properties mentioned, the energy eigenstates easily appear as “the possible” or “the allowed states” of the system, besides which there are no other states. However, this is wrong. The energy eigenstates form a basis of states, and every superposition of several or even an infinite number of them (also known as superposition or linear combination in the state space) is also a possible state of the system.
For further information see state (quantum mechanics) .
Wolfgang Nolting: Basic Course Theoretical Physics 5/1; Quantum Mechanics - Basics . 5th edition. Springer, Berlin Heidelberg 2002, ISBN 3-540-42114-9 , pp. 119 .