Quantum Chemistry

ABC26PH0136 · A particle in three dimensional cubic box of length L has energy of (14h2)/(8mL2) The degeneracy of the state is · 2012 self-practice

ABC26PH1220 · A particle in three dimensional cubic box of length L has energy of (14h2)/(8mL2). The degeneracy of the state is · JUNE 2012 self-practice

ABC26PH0790 · For a particle in one-dimensional box of length L with potential energy V(x) = 0 for L > x > 0 and V(x) = ∞ for x ≥ L and x ≤ 0 an… · 2001-2022 self-practice

ABC26PH0158 · A particle in a 1-dimensional box of length L is perturbed by a delta function potential, delta (x - L/2), in the middle of the box. The… · 2014

ABC26PH0164 · Average value of momentum for the ground state of a particle in a 1-d box is zero because · 2016

ABC26PH1311 · For a particle of mass m in a one-dimensional box of length 2L, the energy of the level corresponding to n = 8 is · JUNE 2016 self-practice

ABC26PH1317 · The degeneracy of the state having energy (27h2)/(8mL2) for a particle in a 3-D cubic box of length L is · JUNE 2016 self-practice

ABC26PH1214 · For non-degenerate perturbation theory for ground state, with E0(0) as zeroth order energy, E0(1) as the first-order perturbation… · DEC 2011 self-practice

ABC26PH1221 · The following are the three statements about perturbation theory (A) Second order perturbation correction to the ground state energy is… · JUNE 2012 self-practice

ABC26PH0133 · Identify which of the following operators is not hermitian? · 2011

ABC26PH1210 · Identify which of the following operators is not hermitian? · DEC 2011 self-practice

ABC26PH0781 · If psi is the eigenfunction to the Hamiltonian operator with alpha as the eigenvalue, then alpha MUST be · 2001-2022 self-practice

ABC26PH1212 · For the eigen states of the hydrogen atom, which of the following relations between the expectation value of kinetic energy (T) and… · DEC 2011 self-practice

ABC26PH0138 · If A and B are non-commuting hermitian operators, all eigenvalues of the operator given by the commutator [A, B] are · 2012

ABC26PH1224 · If A and B are non-commuting Hermitian operators, all eigenvalues of the operator given by the commutator [A, B] are · DEC 2012 self-practice

ABC26PH0139 · The value of commutator [x, px2] is given by · 2012 self-practice

ABC26PH1225 · The value of commutator [x, px2] is given by · DEC 2012 self-practice

ABC26PH0795 · The potential for a particle in a one-dimensional box is given as: V(x) = 0 for 0 ≤ x ≤ L, and V(x) = ∞ elsewhere. The locations of the… · 2001-2022 self-practice

ABC26PH1237 · The operator [x, [x, p2]] is identical with · JUNE 2013 self-practice

ABC26PH0151 · The commutator of the kinetic energy operator, Tx and the momentum operator, px for the one-dimensional case is · 2014

ABC26PH1248 · The commutator of the kinetic energy operator, Tx and the momentum operator, px for the one-dimensional case is · JUNE 2014 self-practice

ABC26PH1269 · The value of the commutator [x, [x, px]] is · JUNE 2014 self-practice

ABC26PH0162 · Two different non-zero operators A and B (A ≠ B) satisfy the relation (A+B)(A-B) = A2 - B2 · 2015

ABC26PH1277 · The eigenfunctions of the Hamiltonian H (H = T + V) of a harmonic oscillator are (where T and V are kinetic energy and potential energy… · JUNE 2016

ABC26PH0165 · For a hermitian operator A, which does NOT commute with the Hamiltonian H, let psi 1 be an eigenfunction of A and psi 2 be an eigenfunction… · 2016

ABC26PH1281 · For a hermitian operator A, which does NOT commute with the Hamiltonian H, let psi 1 be an eigenfunction of A and psi 2 be an eigenfunction… · JUNE 2016 self-practice

ABC26PH1291 · Which of the functions below is a common eigenfunction of d/dx and (d2)/(dx2) operators? · JUNE 2016 self-practice

ABC26PH1296 · If [A, B] = 0 and [A, C] = 0, then which of the following necessarily holds: [A, B and C are operators] · JUNE 2016 self-practice

ABC26PH0173 · A particle is in a state phi = psi 1 + 3 psi 2 where psi 1 and psi 2 are eigenfunctions of the Hamiltonian of the particle with eigenvalues… · 2018

ABC26PH1307 · A particle is in a state phi = psi 1+3 psi 2 where psi 1 and psi 2 are eigenfunctions of the Hamiltonian of the particle with eigenvalues… · JUNE 2016 self-practice

ABC26PH0182 · Let the Hamiltonian H, in one-dimension, be H = px2/2m + V(x). The commutator of H with x, [H, x], is · 2020

ABC26PH0774 · The normalisation constant 'A' for the wavefunction psi (phi) = Ae(im phi) where 0 ≤ phi ≤ 2 pi is: · 2001-2022

ABC26PH0130 · The energy levels for cyclobutadiene are alpha + 2 beta, alpha, alpha and alpha - 2 beta. The delocalization energy in this molecule is: · JUNE 2011 self-practice

ABC26PH0775 · Deduce whether the matrices A and B commute or not. A = 2 1 0 1 B = 1 1 0 1 · 2001-2022 self-practice

ABC26PH1205 · The energy levels for cyclobutadiene are alpha + 2 beta, alpha, alpha and alpha - 2 beta. The delocalization energy in this molecule is: · JUNE 2011 self-practice

ABC26PH0131 · For a certain particle encountering a barrier, the tunneling probability is approximately e-10. If the mass is halved and width of the… · JUNE 2011

ABC26PH0779 · Find the eigenvalues of the following 3 × 3 matrix given that 2 is one of the eigen values. Compute the determinant of matrix using the… · 2001-2022 self-practice

ABC26PH0780 · Which of the following is NOT a solution of the equation (d2x)/(dt2) + omega 2 x = 0 · 2001-2022

ABC26PH0782 · A quantum mechanical particle of mass m free to rotate on the surface of a sphere of radius r is in the state with energy (10ħ2)/(mr2). The… · 2001-2022

ABC26PH1215 · An excited triplet state wave function of hydrogen molecule with the electronic configuration sigma g1 sigma u1 has the following space part · DEC 2011 self-practice

ABC26PH0784 · The function y = xexp (-x2) has a minimum at x = -1/(√(2)). The second derivative of the function at the minimum is · 2001-2022

ABC26PH0787 · If x = x × px = h/(2 pi i)d/dx, then the value(s) of pxx - xpx is/are · 2001-2022

ABC26PH0788 · The maximum of a function Ae-ax2 (A > 0; a > 0) is at x = · 2001-2022 self-practice

ABC26PH0792 · The function f(x)=xe^-x2 has a minimum at · 2001-2022

ABC26PH0793 · The eigenvalue(s) of the matrix 1 2 2 1 is/are · 2001-2022 self-practice

ABC26PH0140 · Combining two real wave functions phi 1 and phi 2 the following functions are constructed: A = phi 1 + phi 2, B = phi 1 + i phi 2, C = phi… · 2012 self-practice

ABC26PH1226 · Combining two real wave functions phi 1 and phi 2 the following functions are constructed: A = phi 1 + phi 2, B = phi 1 + i phi 2, C = phi… · DEC 2012 self-practice

ABC26PH0142 · The difference in energy levels of n = 2 and n = 1 of a particle -in - a one dimensional box is 6 units of energy. In the same units, what… · 2013 self-practice

ABC26PH1233 · The difference in energy levels of n = 2 and n = 1 of a particle-in-a one dimensional box is 6 units of energy. In the same units, what is… · DEC 2012 self-practice

ABC26PH0143 · The wave function psi of a certain system is the linear combination psi = √(1/4) psi 1 + √(3/4) psi 2 where psi 1 and psi 2 are energy… · 2013