Q3. Consider an infinite potential well of width d. In transitions between neighboring values of n, particles of mass that is in a position state as: 2πχ - sin e-iwit d пх f(x. t) = sine-iwot + d (a) Proof that f (x.t) is still normalized for all value of t. (b) Find the probability distribution P(x.t) = |f(x.t)|²

Physics for Scientists and Engineers with Modern Physics
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Chapter40: Quantum Mechanics
Section40.1: The Wave Function
Problem 40.1QQ
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Q3. Consider an infinite potential well of width d. In transitions between neighboring
values of
n, particles of mass that is in a position state as:
2πχ
sin
e-iwit
d
TX
f(x. t) =
-e-iwot +
sin
(a) Proof that f (x. t) is still normalized for all value of t.
(b) Find the probability distribution P(x.t) = |f(x. t)|²
Transcribed Image Text:Q3. Consider an infinite potential well of width d. In transitions between neighboring values of n, particles of mass that is in a position state as: 2πχ sin e-iwit d TX f(x. t) = -e-iwot + sin (a) Proof that f (x. t) is still normalized for all value of t. (b) Find the probability distribution P(x.t) = |f(x. t)|²
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