Quantum Mechanics MCQs Question and Answer in Engineering Physics

The expectation value of the z coordinate, (z), in the ground state of the hydrogen atom (wave function: $${\psi _{100}}\left( r \right) = A{e^{ - \frac{r}{{{a_0}}}}},$$    where A is the normalization constant and $${a_0}$$ is the Bohr radius), is

The resonance widths $$\Gamma $$ of $$\rho ,\,\omega $$  and $$\phi $$ particle resonances satisfy the relation $${\Gamma _\rho } > {\Gamma _\omega } > {\Gamma _\phi }$$   . Their lifetimes r satisfy the relation

The spin' function of a free particle, in the basis in which s_z is diagonal can be written as \[\left[ {\begin{array}{*{20}{c}} 1 \\ 0 \end{array}} \right]\] and \[\left[ {\begin{array}{*{20}{c}} 0 \\ 1 \end{array}} \right]\] with eigen values \[ + \frac{\hbar }{2}\] and \[ - \frac{\hbar }{2}\] respectively. In the given basis, the normalized eigen function of s_y with eigen value \[ - \frac{\hbar }{2}\] is

A one-dimensional harmonic oscillator is in the state $$\psi \left( x \right) = \frac{1}{{\sqrt {14} }}\left[ {3{\psi _0}\left( x \right) - 2{\psi _1}\left( x \right) + {\psi _2}\left( x \right)} \right],$$        where, $${\psi _0}\left( x \right),\,{\psi _1}\left( x \right)$$   and $${\psi _2}\left( x \right)$$  are the ground, first excited and second excited states, respectively. The probability of finding the oscillator in the ground state is

Which one of the following statements concerning the Compton effect is not correct?

Let $$\overrightarrow {\bf{L}} $$ = (L_x, L_y, L_z) denotes the orbital angular momentum operators of a particle and let L₊ = L_x + i L_y and L_- = L_x - i L_y. The particle is in aneigen state of L² and L_z eigen values $${\hbar ^2}\left( {l + 1} \right)$$   and $$\hbar l$$  respectively. The expectation value of L₊L_- in this state is

A one-dimensional harmonic oscillator carrying a charge -q is placed in a uniform electric field $$\overrightarrow {\bf{E}} $$ along the positive X-axis. The corresponding Hamiltonian operator is

A spin half particle is in the state $${S_z} = \frac{{{\hbar ^2}}}{2}.$$  The expectation values of $${S_x},\,S_x^2,\,{S_y},\,S_y^2$$   are given by

Let $$\left| {{\psi _0}} \right\rangle $$ denotes the ground state of the hydrogen atom. Choose the correct statement from those given below.

An electron propagating along the X-axis passes through a slit of width ∆y = 1 nm. The uncertainty in the y-component of its velocity after passing through the slit is