1./10/ A particle is placed in the potential well of finite depth U. The width a of the well is fixed in such a way that the particle has only one bound state with binding energy e = Calculate the probabilities of finding the particle in classically allowed and classically forbidden regions. Uo/2.
1./10/ A particle is placed in the potential well of finite depth U. The width a of the well is fixed in such a way that the particle has only one bound state with binding energy e = Calculate the probabilities of finding the particle in classically allowed and classically forbidden regions. Uo/2.
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Transcribed Image Text:1./10/ A particle is placed in the potential well of finite depth Uo. The width a of the well is
fixed in such a way that the particle has only one bound state with binding energy e =
Calculate the probabilities of finding the particle in classically allowed and classically forbidden
regions.
U/2.
2./10/ Calculate the result of the transformation of the vector operator
projection V, by rotation Ry around an angle a.
Hint: Take the second derivative of the transformed operator with respect to a and solve the second-order
differential equation.
3./20/
Consider the Gaussian wave packet,
(x) = A exp
Por
(1)
where Po and & are real parameters.
a. Show that this wave function can be nornalized,
| dr jv(2)/* = 1,
(2)
%3D
and find the corresponding amplitude A.
b. Find the corresponding wave function, o(p), in the momentum repre-
sentation and check its normalization.
c. Calculate expectation values (r) and (p).
d. Calculate the uncertainties Ar and Ap and their product.
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