moving in one dimension with potential energy 
by
of: a system
is: a differential equation, derived from the time-dependent Schrödinger equation for the system in the case where the wavefunction is separable, whose solutions (called spatial wavefunctions) depend only on spatial variables (i.e. not time) and are the energy eigenfunctions of the system. [M6.4, P10.4]
therefore can be written: as an eigenvalue equation of the total energy operator (the Hamiltonian operator) with eigenvalues that correspond to the possible values of the total energy of the system. [M6.4, P10.4, P11.1]
has: a specific form that depends on the problem in hand.
is exemplified; for a particle of mass moving in one dimension with potential energy by
[M6.4, P10.4, P11.1]
Copyright 1997, The Open University