Test: Quantum Mechanics - 2 - Physics MCQ
20 Questions MCQ Test GATE Physics Mock Test Series 2025 - Test: Quantum Mechanics - 2
An electron with energy 'E' is coming from far left to a potnetial step at x = 0. If E/V =9/8 then ratio of wavelength (λ1/λ2) of electron in region I and II is (Upto two decimal places)
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Wavefunction of a particle iii some one dimension potential is given by,
where k is the positive real constant. Probability of:finding the particle between x = 0 and x = a/4 is _____ %. (Upto two decimal places)
where k is the positive real constant. Probability of:finding the particle between x = 0 and x = a/4 is _____ %. (Upto two decimal places)
Consider the spin state of a system in 
reresentation
What is the average value of the operator 
corresponding to the x-component of the spin.
Find the eigenvalues of the component of spin operator 
of an electron in direction of a unit vector with spherical coordinates 
do not depent on direction 
They are always 
An operator 
operates on a state vector such that 
is known to be existed, then 
represent the total angular momentum operator. The value of 
is
A particle of mass m is being scattered by a potential given by V(r) = 
The differential cross-section calculated by Born's approximation is
Consider a particle in the 1-D potential well given by
Now, a small perturbation is added to the well given as
The first-order correction to the energy of second energy level, is
In a two-dimensional vector space spanned by basis vectors 
Two vectors in this space are given as
An operator 
is represented by matrix.
describes the spin-spin interaction.
For the ground state (n=0), the total harmonic oscillator energy is:
depends on the relative spin orientation:
An electron is placed in an uniform magnetic field 
where 
points in the direction of vector 
The Hamiltonian of the system is H = 
is a constant and 
are pauli matrices Energy of ground state in terms of kB0
A particle of mass 'm' with in box of length L, the wave function of the state is given by
then the energy of the particle of the state is
A linear harmonic oscillator is perturbed by the potential V' (x) = ax2-bx4; a and b constants. If first order energy correction to the second excited energy level is zero then 
in units of 
is (Upto two decimal places)
The wave function of a hydrogen atom is given by 
where 'a0' is Bohr radius and 
is spherical harmonic function for l = 2 and m = 0. If probability of finding the electron is maximum at 'rmp' and average distance between electron and proton is <r> then ratio of the two 
is (upto two decimal places)
Angular frequency for a wave propagating inside a waveguide is given in terms of the wave number K and the width of the guide b as
If group velocity is 3/4th of the velocity then k is
Seven spin -3/2 identical non-interacting particle are subjected to the potential given as
The lowest energy of the system is
A particle of mass 'm' in 1-D harmonic oscillator potential 
In the non-relativistic limit, where the kinetic energy T and momentum P are related as T = p2/2m. The ground state energy is known to be 
For the relativestic corrections in relation between T and P, calculate energy shift in ground state to the order of 1/c2 (c is speed of light in vacuum)
The wave function of a one-dimensional system is given as
where A, n and a are positive constants. The form of the potential if V(x) → 0 
The wavefunction of a hydrogen atom is given by
where a0 is Bohr radius and 
is spherical harmonic function for l = 1 and m = 0. What is the dispersion in the measurement of distance of electron from nucleus?
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Important Questions for Quantum Mechanics - 2
Quantum Mechanics - 2 MCQs with Answers
Online Tests for Quantum Mechanics - 2 GATE Physics Mock Test Series 2025
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