A particle is represented by the following wave function:
ψ(x) =0 | x<−1/2 | |
ψ(x) =C(2x + 1) | −1/2 < x < 0 | |
ψ(x) =C(−2x + 1) | 0 < x < +1/2 | |
ψ(x) =0 | x > +1/2 |
(a)Evaluate the probability to find the particle between x=0.19 and
x=0.35.
(b) Find the average values of x and x2, and the
uncertainty of x:
Δx=√(x2)av-(xav)2
xav= | |
(x2)av= | |
Δx = |
A particle is represented by the following wave function: ψ(x) =0 x<−1/2 ψ(x) =C(2x +...
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The wave function of a restricted particle on the x-axis is between x = 0 and x = 1 ψ= ax ^2 and everywhere else ψ = 0. a) Find the value of constant a b) Find the probability that the particle is between x = 0.1 and x = 0.2 c) Find the wait value for the position of the particle
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A. Momentum space We define the momentum space wave function φ(p) as where Ψ(x)is a solution of the Schrödinger equation in configuration (position) space a) Show that the expectation values of and p can be written in terms of Ф(p) as <p(p)p(p)dp b) Demonstrate that φ(p) is normalized, ie if Ψ(x) is normalized. J ΙΨ(2)12dr-1 c) Show that Ф(p) 2dp can be interpreted as the probability to find a particle with momen tum between p and p+ dp
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