Quantum Mechanics Answers

Prove that the three triplet states are all symmetric and the singlet state is antisymmetric.

For a simple harmonic oscillator, show that the expectation value of x, defined as <x>mn = ∫ Ψ*m (x) Ψ n(x) dx is √1/2a^2 for the n=0 and m=1states.Use the

result ∞∫0 x^1/2 exp ^-x dx= √π 

Three packing crates of masses, M1 = 6 kg, M2 = 2 kg 

and M3 = 8 kg are connected by a light string of 

negligible mass that passes over the pulley as shown. 

Masses M1 and M3 lies on a 30o

incline plane which

slides down the plane. The coefficient of kinetic friction 

on the incline plane is 0.28. 

A. Draw a free body diagram of all the forces acting in the masses M1 and M2.

Consider Harmonic oscillator Hamiltonian in 2-D

(P_x)^2/2+(p_y) ^2/2+x²/2+y^2/2+lamda×x×y

Find the ground state energy and energy of first exited state

Consider H cap=(p_x) ^2/2+x²/2+x×(p_x) , find out the eigen energy state of Hamiltonian

The wave function of a particle in an infinite square well of width 2a (-a to a) is given by,

Ψ(x) = (1/a)^1/2 cos (3πx/2a)

Determine <x^2> for the particle.

A particle of mass m and zero energy has a wave function Ψ (x)= Nx exp -x^2/16 , where

N is a constant. Determine the potential energy V (x) for the particle.

If a light with a frequency of radiation of 8×10^14 Hz is shone on metal and photoelectron are ejected with a maximum kinetic energy of 1.6×10^-19 J, what is work function of the material ?

He+: Using Bohr’s model, give the expression for the energy levels in the He+ ion.

(a) What is the binding energy of this ion?

(b) Give the expression of line spectrum for this ion in terms of the Rydberg constant.

(c) What is the longest wavelength for the first four series of this line spectrum.

Determine the wavelength of proton that has been accelerated through a pd of 200V.