STATIONARY STATES

The solution of the time-dependent part of the Schrodinger Equation (1)

.......(1)

is simple and written as:

.........(2)

...............(3)

From Equation (3), the wave function can now be written as:

..........(4)

and the probability density of the previous wave function is:

ρ(x, t) = |Ψ(x, t)|² = ψ(x)ψ(x)^∗ = constant .......(4)

Thus, the probability density of the wave function is independent of time. Such quantum states are called stationary states. As the word stationary implies, the probability of finding the particle at all points in space will remain constant in time, as if the particle is stationary, or in other words, “the particle is frozen in time.” In these states, the measurement of a particle’s energy would yield an exact value. Such states are also called energy eigenstates and determinate states.