List of top Physics Questions on Quantum Mechanics asked in IIT JAM PH

A particle of mass \( m \) is in an infinite square well potential of length \( L \). It is in a superposed state of the first two energy eigenstates, as given by \( \psi(x) = \frac{2}{\sqrt{3L}} \psi_1(x) + \frac{2}{\sqrt{3L}} \psi_2(x) \). Identify the correct statement(s). \( h \) is Planck’s constant.
A proton is confined within a nucleus of size \( 10^{-13} \, \text{cm} \). The uncertainty in its velocity is ........... \( \times 10^8 \, \text{m/s} \).
Given the wave function of a particle \( \psi(x) = \sqrt{\frac{2}{L}} \sin \left( \frac{\pi x}{L} \right) \) for \( 0<x<L \) and 0 elsewhere, the probability of finding the particle between \( x = 0 \) and \( x = L/2 \) is .............
For a quantum particle confined inside a cubic box of side \( L \), the ground state energy is given by \( E_0 \). The energy of the first excited state is
A particle of mass \( m \) is placed in a three-dimensional cubic box of side \( a \). What is the degeneracy of its energy level with energy \( \frac{14 \hbar^2 \pi^2}{2m a^2} \)?
A particle of unit mass is moving in a one-dimensional potential \( V(x) = x^2 - x^4 \). The minimum mechanical energy (in the same units as \( V(x) \)) above which the motion of the particle cannot be bounded for any given initial condition is:
Consider a one-dimensional harmonic oscillator of angular frequency \( \omega \). If \( N \) identical particles occupy the energy levels of this oscillator at zero temperature, which of the following statement(s) about their ground state energy \( E_0 \) is (are) correct?