Show directly that the trial wave function (x, t) = e(kx-wt) satisfies in- The derivatives are (Use the following as necessary: Y, k, and w.) i(kx-cot) and 24 at a²4 ax² hwy = -iwe The result is -K²e²l k²i(kx-cot) -w+Vy 2m X Substituting in the time-dependent Schrödinger equation gives (Use the following as necessary: , p and m.) X a4(x, t) at + VY ²a²(x, t) 2m ax² + √(x, t). E = K + V where K is the kinetic energy, which is a statement of conservation of mechanical energy.
Show directly that the trial wave function (x, t) = e(kx-wt) satisfies in- The derivatives are (Use the following as necessary: Y, k, and w.) i(kx-cot) and 24 at a²4 ax² hwy = -iwe The result is -K²e²l k²i(kx-cot) -w+Vy 2m X Substituting in the time-dependent Schrödinger equation gives (Use the following as necessary: , p and m.) X a4(x, t) at + VY ²a²(x, t) 2m ax² + √(x, t). E = K + V where K is the kinetic energy, which is a statement of conservation of mechanical energy.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:Show directly that the trial wave function (x, t) = e(kx-wt) satisfies in-
The derivatives are (Use the following as necessary: Y, k, and w.)
i(kx-cot)
and
24
at
2²
əx²
hwy =
-iwe
The result is
-kei(kx-cot)
2
-y + Vy
2m
X
X
a4(x, t)
at
Substituting in the time-dependent Schrödinger equation gives (Use the following as necessary: Y, p and m.)
+ VY
=
ħ² a²(x, t)
2m əx²
+ VY(x, t).
E = K + V
where K is the kinetic energy, which is a statement of conservation of mechanical energy.
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