Quantum Mechanics Answers

For hydrogen, an electron is in 2p state. Obtain the magnitude of orbital angular momentum and possible

z-components of orbital angular momentum 𝐿⃗ . What would be the possible values of total angular

momentums (𝐽 ) and associated magnetic moments 𝜇𝐽

⃗⃗⃗

A 2-kg steel ball is attached to the end of a flat strip of metal that is clamped at its base. If the spring constant is 8 N/m, the frequency of vibration will be approximately?

A particle of mass m is confined between 0<=x<=l. If px be the momentum, then find px in the ground state

Derive schrodingers equation

If the energy of electron in second excited state is 9eV in an infinite potential box . The ground state energy of the particle is:

If A and B are Hermitian operators, show that AB is Hermitian if and

only if A commutes with B

 If A and B are Hermitian operators, show that AB is Hermitian if and only if A commutes with B

Let A and B be two non-commuting Hermitian operators. Determine

which of the following operators are Hermitians:

(a) AB

(b) [A, B]

(c) {A, B} = AB + BA

(d) ABA

(e) An where n is an integer.

 If A, B and C are Hermitian operators, determine if the following combinations are Hermitian: (a) A + B (b) 1 2i [A, B] (c) (ABC − CBA) (d) A2 + B2 + C 2 (e) (A + iB)

A Hermitian operator Aˆ has only three normalized eigenfunctions ψ1, ψ2, ψ3, with corresponding eigenvalues a1 = 1, a2 = 2, a3 = 3, respectively. For a particular state Φ of the system, there is a 50% chance that a measure of A produces a1 and equal chances for either a2 or a3. (a) Calculate hAi. (b) Express the normalized wave function Φ of the system in terms of the eigenfunctions of Aˆ.