A particle in a central potential V (r) has a wavefunction of Ψ= f (r,Ө) sin2Ø where Ø is the azimuthal angle in the spherical polar coordinate system. Also, this wavefunction Ψ is properly normalized, i.e.˂ΨӏΨ˃=1Read the following passage to answer the given questions based on it. Choose the correct options. (Marks: 1)What is the probability of measuring Lz and obtain 2ħ?OPTIONS 0.056 0.05 0.52 0.6

A particle in a central potential V (r) has a wavefunction of Ψ= f (r,Ө) sin2Ø where Ø is the azimuthal angle in the spherical polar coordinate system. Also, this wavefunction Ψ is properly normalized, i.e.˂ΨӏΨ˃=1Read the following passage to answer the given questions based on it. Choose the correct options. (Marks: 1)What is the expectation value of z component of orbital angular momentum , ˂Lz ˃?OPTIONS 0.016 0.015 0.021 0.017

The wave function for a quantum particle is given by𝜓(x)= Axbetween x = 0 and x = 1.00, and 𝜓(x) = 0 elsewhere.Find the value of the normalisation constant A.Answer for part 1 Find the expectation value of the particle's position.Answer for part 2Find the probability that the particle will be found between x = 0.245 and x = 0.465.

PASSAGEConsider a particle whose wave function is,Read the following passage to answer the given questions based on it. Choose the correct options. (Marks: 1)Find the total angular momentum of this particleOPTIONS √2ħ √6ħ2 √6ħ √2ħ2

6.Question 6Suppose we have a particle in 1-dimension, with wavefunction 𝐴𝑒−∣𝑥∣2𝑑Ae − 2d∣x∣​ .What is the probability to find the particle in the interval [0,𝑑][0,d]?Please provide your answer in terms of 𝐴A, 𝑑d, mathematical constants such as 𝜋π (entered as 1pi) or 𝑒e (entered as 1e).(Assume that A is real)1 point0.5*(1-e^-1)A^2*d*(1-exp(-1))A^2*d*(1-e^-1)0.5*(1-exp(-1))

A particle in a one dimensional infinite square well (box) is in a superposition of two quantum states:1 21234   where1 2and  are orthogonal, normalized (ortho-normal) eigenfunctions of the Hamiltonian.(a) Calculate the new normalization constants for1 2and  . [2 marks](b) A measurement of energy is made. What is the probability that the measurement will find energy1E ?What is the probability that the measurement will find energy2E ? [2 marks](c) Write down the integral expression for the evaluation of the expectation value of position,x - evaluateany “trivial” integrals, but leave as integrals any that require a full solution. [2 marks](d) Write down the integral expression for the evaluation of the expectation value of momentum,xp -evaluate any “trivial” integrals, but leave as integrals any that require a full solution