Conditions on wave functions We consider solutions psi of the time-independent S

Question

Conditions on wave functions We consider solutions psi of the time-independent Schrodinger equation in one dimension: [-h^2/2m d^2/dx^2 + V(x)] psi(x) = E psi (x) Remember that psi must satisfy the time-independent Schrodinger equation as well as the conditions: psi (x) is a continuous function of x d psi(x)/dx can be discontinuous only when the potential is infinite in an infinitesimally small region psi must be normalizable (i.e. square-integrable) Below we consider several piecewise constant potentials. We have sketched wave functions (thick blue lines) that may or may not be allowable solutions. In each case, indicate if the solution is acceptable. If not, indicate what is wrong with the wave function.

Explanation / Answer

Acceptable wavefunction are: a, b,c,e,f

D: Derivative of wavefunction is not discontinuous at x=0 where potential become infinite.

g) Wavefunction is not square integrable as wavefunction tend to infinity as x tends to infinity

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