37 Official GATE PH Questions with Verified Solutions & Answer Keys
It is necessary to apply quantum statistics to a system of particles if (A) there is substantial overlap between the wavefunctions of the particles. (C) the particles have identica...
For a physical system, two observables O, and O, are known to be compatible. Choose the correct implication from amongst those given below: (A) Every eigenstate of O, must necessar...
An exact measurement of the position of a simple harmonic oscillator (SHO) is made with the result x =Xo. [The SHO has energy levels E, (n =0,1,2,...) and associated normalized wav...
The expectation value of the momentum, in this state is (A) ha (B) nVa (C) a (D)...
The valence clectrons do not directly determine the following property of a metal. (A) Electrical conductivity (B) Thermal conductivity (C) Shear modulus (D) Metallic lustre 0.6 Co...
0.9 The Bloch theorem states that within a crystal, the wavefunction, @(F), of an clectron has the form (A) w(r) = «(r)e where «(7) is an arbitrary function and k is an arbitrary v...
The Bloch theorem states that within a crystal, the wavefunction, \psi(\vec{r}), of an electron has the form (A) \psi(\vec{r}) = u(\vec{r})e^{i\vec{k}\cdot\vec{r}} where u(\vec{r})...
Which of the following is an allowed wavefunction for a particle in a bound state? Nis a constant and a, B> 0. (A) WEN$ (B) yr= N(1-ear) (C) W= Ne""'eAity+*) ( v e(mnen zero consta...
A particle of mass m is confined in the poiential V(x) = -mc"x' for x >0, V(x) for x S0. Let the wavefunction of the particle be given by W(0) =-7540+-3543- where y, and yf, are th...
The effective mass of electrons in the band is given by (A) rả cos(ka) (B) Zya cos(ka) (C) tỉ (D) rả sin(ka) 2rả sin(ka) PH 11/20 2011 PH Linked Answer Questions Statement for Link...
Consider the wavefunction 1 2 , s r r for a fermionic system consisting of two spin-half particles. The spatial part of the wavefunction is given by, 1 2 1...
The ground state wavefunction for the hydrogen atom is given by 0 3/2 / 100 0 1 1 4 r a e a - , where a0 is the Bohr radius. The plot of the radial probability de...
At a certain temperature T, the average speed of nitrogen molecules in air is found to be 400 m/s. The most probable and the root mean square speeds of the molecules are, respectiv...
Which one of the following commutation relations is NOT CORRECT ? Here, symbols have their usual meanings....
A spin-half particle is in a linear superposition 0.8|↑〉 + 0.6|↓〉 of its spin-up and spin-down states. If |↑〉 and |↓〉 are the eigenstates of ߪ then what is the expectation value, u...
Consider the wave function AinL(_0/r), where Ais the normalization constant. For r = 2_0, the magnitude of probability current density up to two decimal places, in units of (A݉/kis...
At a given temperature, T, the average energy per particle of a non -interacting gas of two-dimensional classical harmonic oscillators is ________________ kBT (kB is the Boltzmann ...
An electron in the ground state of the hydrogen atom has the wave function Ѱ(𝑟𝑟⃗) = 1 �𝜋𝜋𝑎𝑎0 3 𝑒𝑒−�𝑟𝑟 𝑎𝑎0� � where 𝑎𝑎0 is constant. The expectation value of the opera...
A one dimensional harmonic oscillator is in the superposition of number states, n , given by 32 322 1 + =ψ . The average energy of the oscillator in the given state is ____________...
The Pauli matrices for three spin-½ particles are ô,, 02, and o3, respectively. The dimension of the Hilbert space required to define an operator Ô=õ, \cdotô, xô, is...
Let L and p be the angular and linear momentum operators, respectively, for a particle. The commutator [Lx, P,] gives (B) 0 (C) it px (D) itip= (A) - it p=...
Suppose a linear harmonic oscillator of frequency c and mass m is in the state at t = 0 where (Vo) and (41) are the ground and the first excited states, respectively. The value of ...
Which of the following operators is Hermitian? (A) d dx d (B) dx (c) i22 dx? d' (D) PH 2/10 GATE 2016 Physics...
If $, and 5, are the spin operators of the two electrons of a He atom, the value of (5, \cdot5,) for the ground state is (1) -33 (B) - 3 (C) 0 (D)...
The degeneracy of the third energy level of a 3-dimensional isotropic quantum harmonic oscillator (A) 6 (B) 12 (C) 8 (D) 10...
The electronic ground state energy of the Hydrogen atom is -13.6 eV. The highest possible electronic energy eigenstate has an energy equal to (A) 0 (B) leV (C) +13.6 eV (D) 00...
Which one of the following operators is Hermitian? Correct: 2 Wrong : -0.66 2 2 (C) eiPxa (D) e iPra...
The Hamiltonian for a quantum harmonic oscillator of mass $m$ in three dimensions is $H = \frac{p^2}{2m} + \frac{1}{2}m\omega^2 r^2$, where $\omega$ is the angular frequency. The e...
Consider a rectangular potential barrier $V(x) = V_0$ for $a < x < b$ and 0 elsewhere, with $V_0 > 0$. For particles of energy $E < V_0$ incident on this barrier from the left ($x ...
S, denotes the spin operator defined as S = (i d Which one of the following is correct? The eigenstates of spin operator 5, are /1% 6) and (4),= (;) The eigensates of spin operator...
Consider a particle in a one-dimensional infinite potential well with its walls at x = 0 and x = L. The system is perturbed as shown in the figure. 00 _ V (L) = Vo V (0) = 0 x = 0 ...
An electromagnetic pulse has a pulse width of 10-3 s. The uncertainty in the momentum of the corresponding photon is of the order of 10- kg m s-1, where N is an integer. The value ...
Consider a particle in three different boxes of width L. The potential inside the boxes vary as shown in figures (i), (ii) and (iii) with V_0 ≪ ℏ^2\pi^2 _2^2 . The corresponding gr...
A particle of mass m is moving inside a hollow spherical shell of radius a so that the potential is V(r) = 0 for r < a ∞ for r ≥ a The ground state energy and wavefunction of the p...
Consider a particle in a two dimensional infinite square well potential of side L, with 0 ≤ x ≤ L and 0 ≤ y ≤ L. The wavefunction of the particle is zero only along the line y = L ...
A particle of mass m in an infinite potential well of width a is subjected to a perturbation, V' = ℎ2 40ma2 as shown in figure, where ℎ is Planck's constant. The first order energy...
Let |m〉 and |n〉 denote the energy ei genstates of a one -dimensional simple harmonic oscillator . The position and momentum operators are X̂ and P̂, respectively. The matrix elemen...