Test: Quantum Mechanics - 1 - Physics MCQ

Consider a system whose initial state at r = 0 is given in term of a complete and orthonormal set of three vectors  as follows  the probability of find tlie system at tune t in state  is _______ (upto two decunalplaces)

An election is confined in an infinite square well of width 10x10^-15 m. Calculate the wavelength of the electron emitted when the proton undergoes a transition from the first excited state (n=2) to the ground state (n=1).​

Consider a tliree dimensional harmonic oscillator with Hamiltonian

The number of distinct eigenstates with energy eigenvalue 5/2 ℏω is_________
(Answer should be an integer).

Consider an operator  for a system of total angular momentum j = 1 then winch of the following state having non zero uncertainty

In the simple harmonic oscillator

what are the condition on m and m' for  to be non-zero 

Find the differential cross-section for die scattering of slow (low velocity) particle from a spherical delta poten- tial V (r) = V₀ δ (r - a)

For case of  n = 2, ℓ = 1, m = 0 the value of r at which the radial probability density of the hydrogen atom reaches its maximum is ____ a₀.  (answer should be an integer)

Consider a system winch is mtially in the state  was measured with value -ℏ, the probability is_______(upto one decimal place) 

An electron is confined in the ground state of a one dimensional harmonic oscillator such that  energy required to excite to its first excited state is _____ (MeV)

A particle of mass m coming in from the left with energy E > 0, encounters barrier potential

The wave function is given by


The constant A and B satisfy which one of the following relation?

Calculate the width of the probability density distribution for r(i.e Br) for hydrogen atom for the state 

At t = o, a state is given by

Where are ortlionomial stationary states of energy E_l & E₂ respectively with E₂ > E_l what is the shortest tune T > 0 for w hich is orthogonal to

If the state of a particle moving in one dimensional harmonic oscillator is given by

Where represent the normalized n^th energy eigenstate find the expectation value of  number operator  ( n = 0,1,2,3....)

A particle of mass m moves in a one dimensional potential box

Consider the V₀ part as perturbation, using first order perturbation method calculate the energy of ground state.

A spin state precesses in a magnetic field same way as the classical magnetic dipole precesses in magnetic field with lasmor frequency given by  consider the Hamiltonian  Larrnor frequency  is (in tem is of ω₀)
(answer should b e an mteger)

Consider a system of four non-interacting identical spin 1/2 particles that are in same state  and confined to move in a one-diniension infinite potential well of length a: V(x) = 0 for 0 < x < a and V(x) = ∞ forotlier values of x. The ground state energy of the system in units of is (answer should be an integers).

Consider a system whose intial state and hamiltonian are given by

find the total energy of a system