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 .

Consider two eigenstates |𝑢1

⟩ and |𝑢2

⟩ of an observable satisfy the 

condition ⟨𝑢1

|𝑢2

⟩ = 4 and ⟨𝑢1

|𝑢1

⟩ = ⟨𝑢2

|𝑢2

⟩ = 1. Find a normalized 

linear combination of |𝑢1

⟩ and |𝑢2

⟩ ,i.e., (𝑎|𝑢1

⟩ +

𝑏|𝑢2

⟩, where a and b are real constant) which is orthogonal to (|𝑢1

⟩ −

|𝑢2

⟩).

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.

In an air standard diesel cycle the state before the compression is 100kPa and 300K. A peak pressure of

6000kPa and a maximum temperature of 2400K exist in the cycle. Find the compression ratio, efficiency

and mean effective pressure of the cycle.

the drawing, the weight of the block on the table is 422 N and that of the hanging block is 185 N. Ignoring all 

frictional effects and assuming the pulley to be massless, 

𝑂2𝜓(𝑥) =xd𝜓(𝑥)/dx

Is 𝑂4𝜓(𝑥) = 𝜓(𝑥)* a linear operator?

Find [O4,O2]

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.