20.4.11 The ordinary space wave function (r.1) satisfies the time-dependent Schrödinger equation, a(r, 1) Ər ħ² ih 2m Show that the corresponding time-dependent momentum wave function satisfies the analogous equation -V² + V(r). ap(p. 1) p² at -9 + V (ih Vp)❤. 2m Note. Assume that V(r) may be expressed by a Maclaurin series and use Exer- cise 20.4.10. V(ihVp) is the same function of the variable iħ V, that V(r) is of the variable r..
20.4.11 The ordinary space wave function (r.1) satisfies the time-dependent Schrödinger equation, a(r, 1) Ər ħ² ih 2m Show that the corresponding time-dependent momentum wave function satisfies the analogous equation -V² + V(r). ap(p. 1) p² at -9 + V (ih Vp)❤. 2m Note. Assume that V(r) may be expressed by a Maclaurin series and use Exer- cise 20.4.10. V(ihVp) is the same function of the variable iħ V, that V(r) is of the variable r..
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Mathematical Physics
Topic: Fourier Transform
Transcribed Image Text:20.4.11
The ordinary space wave function (r.1) satisfies the time-dependent Schrödinger
equation,
a(r, 1)
Ər
ħ²
2m
iħ
Show that the corresponding time-dependent
analogous equation
ap(p. 1) p²
at
-V²y + V(r).
momentum wave function satisfies the
-9 + V (ih Vp).
2m
Note. Assume that V(r) may be expressed by a Maclaurin series and use Exer-
cise 20.4.10. V (iħVp) is the same function of the variable iħ V, that V(r) is of the
variable r..
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