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 10 2mr2. The… · 2001-2022
ABC26PH1215 · An excited triplet state wave function of hydrogen molecule with the electronic configuration 1 1 has the following space part · DEC 2011self-practice
ABC26PH0784 · The function y=x (-x2 ) has a minimum at x=-1√(2). The second derivative of the function at the minimum is · 2001-2022
ABC26PH0786 · [-h2 (8 pi 2 m ) dd x2+h2 alpha 2 x2 (2 pi 2 m ) ] (- alpha x2 )=C h2 (4 pi 2 ) (- alpha x2 ), where h, pi , m and alpha are constants… · 2001-2022
ABC26PH0787 · If x=x px=h/(2 pi i) d/dx, then the value(s) of px x-x px is/are · 2001-2022
ABC26PH0788 · The maximum of a function Ae^-ax2(A>0 ; a>0) is at x= · 2001-2022self-practice
ABC26PH0791 · Which of the following set(s) of quantum numbers is (are) NOT allowed? · 2001-2022self-practice
ABC26PH0792 · The function f(x)=xe^-x2 has a minimum at · 2001-2022
ABC26PH0793 · The eigenvalue(s) of the matrix [arrayll 1 & 2 \\ 2 & 1 array ] is/are · 2001-2022self-practice
ABC26PH0140 · Combining two real wave functions 1 and 2 the following functions are constructed: A=1 +2, B=1+i 2, C=1-i 2, D=i (1+2 ) The correct… · 2012self-practice
ABC26PH1226 · Combining two real wave functions 1 and 2 the following functions are constructed: A=1+2, B=1+i 2, C=1-i 2, D=i (1+2 ) The correct… · DEC 2012self-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 is the… · 2013self-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 2012self-practice
ABC26PH0143 · The wave function of a certain system is the linear combination =√(1/4)\,1+√(3/4)\,2 where 1 and 2 are energy eigen functions with eigen… · 2013
ABC26PH1234 · The wave function of a certain system is the linear combination =√(1/4) 1+√(3/4) 2 where 1 and 2 are energy eigen functions with eigen… · JUNE 2013self-practice
ABC26PH1235 · For the particle-in-a-box problem in (0, L) an approximate wave function is given as x(L / 2-x)(L-x). The average energy E for such a state… · JUNE 2013self-practice
ABC26PH1238 · For the particle-in-a-box problem in (0, L) the value of x3 in the n limit would be · JUNE 2013self-practice
ABC26PH0145 · In the formation of H2 molecules from 2 H atoms placed at positions A and B , and separated by a distance rAB, a part of special… · 2013
ABC26PH1240 · In the formation of H2 molecules from 2H atoms placed at positions A and B, and separated by a distance rAB, a part of special wave… · JUNE 2013self-practice
ABC26PH0152 · Consider a particle confined in a cubic box. The degeneracy of the level, that has an energy twice that of the lowest level, is · 2014
ABC26PH1249 · Consider a particle confined in a cubic box. The degeneracy of the level, that has an energy twice that of the lowest level, is · JUNE 2014self-practice
ABC26PH0153 · If the ionization energy of H atom is x, the ionization energy of Li2+ is · 2014
ABC26PH1253 · If the ionization energy of H atom is x , the ionization energy of Li2+ is · JUNE 2014self-practice
ABC26PH0159 · A quantum particle with fixed initial energy E0<V is allowed to strike the following four barriers separately. The transmission probability… · 2014
ABC26PH1261 · A quantum particle with fixed initial energy E0<V is allowed to strike the following four barriers separately. The transmission probability… · JUNE 2014self-practice
ABC26PH1264 · An eigen state of energy satisfy H =En . In the presence of an extra constant potential V0 · JUNE 2014self-practice
ABC26PH0161 · The simplest ground-state VB wave function of a diatomic molecule like HCl is written as =(1 s, 1) (3 pz, 2 )+B where B stands for · 2015
ABC26PH1265 · The simplest ground-state VB wave function of a diatomic molecule like HCl is written as =(1 s, 1) (3 pz, 2 )+B where B stands for · JUNE 2014self-practice
ABC26PH1267 · Compare the difference of energies of the first excited and ground states of a particle confined in (i) a 1-d box (1 ), (ii) a 2-d square… · JUNE 2014self-practice
ABC26PH1270 · A particle is in a one-dimensional box with a potential Vo inside the box and infinite outside. An energy state corresponding to n=0 ( n=… · JUNE 2014self-practice
ABC26PH0163 · The degeneracy of an excited state of a particle in 3-dimensional cubic box with energy 3 times its ground state energy is · 2015
ABC26PH1272 · The degeneracy of an excited state of a particle in 3-dimensional cubic box with energy 3 times its ground state energy is · JUNE 2014self-practice
ABC26PH1278 · For a particle of mass m confined in a rectangular box with sides 2 a and a , the energy and degeneracy of the first excited state… · JUNE 2016self-practice
ABC26PH1290 · Consider a particle in its ground state confined to a one-dimensional box in the interval (0, ). The probability of finding it between… · JUNE 2016self-practice
ABC26PH1299 · The correct statement about the difference of second and first excited state energies ( Delta E) of a particle in 1-D, 2-D square and 3-D… · JUNE 2016
ABC26PH0170 · The transition moment integral for a rotational transition between J=1 ; MJ=0 and J=2 ; MJ =0 states for a diatomic molecule along the z… · 2018
ABC26PH1302 · The transition moment integral for a rotational transition between J=1 ; MJ=0 and J=2 ; MJ=0 states for a diatomic molecule along the… · JUNE 2016self-practice
ABC26PH1304 · Which of these is not a suitable unnormalized wave function for the excited 1s 2s electron configuration of the helium atom ? · JUNE 2016
ABC26PH1305 · Two opposite sides (in the y direction) of a square box of side L are slightly stretched. Consider the following four statements: A. The… · JUNE 2016
ABC26PH1310 · The lowest energy unnormalized wave function of H2+molecule is (r1 . and r2 are the distances between the electron and nuclei 1 and 2… · JUNE 2016self-practice
ABC26PH1318 · The spatial part of the dominant resonance structure of the LiH molecule is (only valance part of the wave function is shown). · JUNE 2016self-practice
ABC26PH0176 · The function, which is NOT an eigenfunction of the indicated operator, is · 2020self-practice
Variation Method
ABC26PH0141 · The trial wave function of a system is expanded as =c1 1+c2 2. The matrix elements of the Hamiltonian are 1 | H |1 =0 ; 1 | H |2 =2.0= 2 |… · 2012
ABC26PH1227 · The trial wave function of a system is expanded as =c1 1+c2 2. The matrix elements of the Hamiltonian are 1 H 1=0 ; phi 1 H phi 2=20=2 H 1… · DEC 2012self-practice
ABC26PH0160 · For some one-electron system with l=0 and m=0, the functions N0 e- sigma and N1(2- sigma )e- sigma refer respectively to the ground (E0)… · 2014
ABC26PH1262 · For some one-electron system with l=0 and m=0, the functions N0 e- sigma and N1(2- sigma ) e- sigma refer respectively to the ground (E0 )… · JUNE 2014self-practice
ABC26PH1279 · Choosing some Hamiltonian H and an orthonormal basis, a linear variation is carried out to get approximately energies Ej With 2 basis… · JUNE 2016self-practice
ABC26PH1294 · Given a trial wave function =C1 1+C2 2 and the Hamiltonian matrix elements. 1* H 1 dv=0, 1* H 2 dv=2.5, 2* H 2 dv=12.0 the variationally… · JUNE 2016self-practice
ABC26PH1312 · The energy functional from a trial wave function is E( alpha )= ( alpha 3-3 alpha ) / 6. The variationally optimized energy is · JUNE 2016self-practice
ABC26PH0178 · In linear variation method using two orthogonal basis functions, the two roots obtained are 0 and 1 (0<1). The correct relation of these… · 2019