Quantum Mechanics Answers

The wave function of a particle is 𝜓(𝑥) = { 𝐴𝑐𝑜𝑠( 2𝜋𝑥 𝐿 ) 𝑓𝑜𝑟 − 𝐿 4 ≤ 𝑥 ≤ 𝐿 4 0 elsewhere i) Determine the normalization constant A. ii) What is the probability that the particle will be found between x= 0 and x = L/6 if we measured its position? iii) Find the expectation values for the operators x, p, and p 2 .

The Potential Step (E > U0):

(a) Express the reflection and transmission probabilities in terms of E and U0. What is the probability

that the incident particle will be reflected for the case U0 = 0.7 E?

(b) Obtain the probability density and the real and imaginary parts of the wavefunction for t = π/2 ω .

Also, plot them.

Calculate the ground state energy for delta function potential by making use of variational principle.

Use the variational principle to obtain an upper limit to ground state energy of a particle in one dimensional box.

How are wireless smart sensor networks based on quantum tunneling?

Construct the symmetric and antisymmetric combinations of the degenerate functions.

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