a) Derive the following commutator relationships between the components of angular momentum L and of p:...
a) Derive the following commutator relationships between the components of angular momentum L and of p:
(i) [Ly, px] = −ih(bar)pz
(ii) [Ly, pz] = ih(bar)px
(iii) [Ly, p2x ] = −2ih(bar)pxpz
(iiii) [Ly, p2z ] = 2ih(bar)pxpz
(b) Hence show that the square L2 of the angular momentum operator L commutes with the kinetic energy operator
p2/2m = (p2x + p2y + p2z )/2m.
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a) Derive the following commutator relationships between the
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3. An operator  is Hermitian if it satisfies the condition $ $(y) dx = (Ap) u dx, for any wavefunctions $(x) and y(x). (i) The time dependent Schrödinger equation is ih au = fu, at where the Hamiltonian operator is Hermitian. Show that the equation of mo- tion for the expectation value of any Hermitian operator  is given by d(A) IH, Â]), dt ħi i = where the operator  does not depend explicitly on time....
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