7. Consider a particle with normalized wave function S Nxe-/2 if 0

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7. Consider a particle with normalized wave function
S Nxe-/2 if 0<x<∞
V(x) :
elsewhere,
where a is a positive real constant and N = /a³/2.
(a) Write down an expression for the probability of finding the particle
between x and x+ dx. Illustrate how this probability depends on x
and find the most probable value of x.
(b) Find the expectation values for the position and the square of the
position, (x) and (x²).
Transcribed Image Text:7. Consider a particle with normalized wave function S Nxe-/2 if 0<x<∞ V(x) : elsewhere, where a is a positive real constant and N = /a³/2. (a) Write down an expression for the probability of finding the particle between x and x+ dx. Illustrate how this probability depends on x and find the most probable value of x. (b) Find the expectation values for the position and the square of the position, (x) and (x²).
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