Schrödinger Wavefunctions in a Continuously Varying Potential

quantum number n

1

This Demonstration shows solutions of the one-dimensional Schrödinger equation in a potential-energy field

V(x)

, which can be varied by moving a series of locators. A quantum number

n

(from 1 to 20) can be selected. The Schrödinger equation is then solved numerically for the wavefunctions

ψ

n

(x)

, which are plotted in red, in arbitrary units. The black curves show the corresponding probability densities



ψ

n

(x)

2

|

. The potential energy

V(x)

is scaled in units of

100

2

ℏ

/2m

.