Schrodinger's equation and potential energy

xiankai · Mar 24, 2007

Homework Statement

1. In a region of space, a particle with zero total energy E has a wavefunction

ψ (x) = A x exp - (x2/L2)

a) Find the potential energy U as a function of x
b) Make a sketch of U(x) versus x

Homework Equations

time independent Schrödinger's equation

Time-independent Schrödinger equation: second derivative of ψ with respect to x equals negative 2m over ħ squared, times (E minus U), times ψ.

The Attempt at a Solution

Handwritten derivation of the potential U(x) from the wavefunction psi(x) = Axe^(-x^2/L^2), taking first and second derivatives and substituting into the Schrodinger equation, ending with U(x) = (4 hbar^2/(2mL^4))x^2 - 6 hbar^2/(2mL^2).

judging by the nature of the equation, the graph of U(x) against x seems to be that of a quadratic curve with the minimum point below the y-axis.

did i get it correct? I am abit uncertain...

Dick · Mar 24, 2007

That looks fine to me.

Schrodinger's equation and potential energy

Homework Statement

Homework Equations

The Attempt at a Solution

Discussion

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