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ONLINE TEST -2, B.Sc-3" Year, , Quantum Mechanics, , , , 1. The wave function of box of particle is given by, , (a) Asinkx, (b) Bcoskx, (c) Asinkx + Bcoskx, (d) Asinkx — Bcoskx, , 2. The potential of free particle is, , (a) maximum (b) minimum (c) zero (d) infinite, , 3. Hamiltonian is given by, (a) Difference of K.E and P.E, (b) Product of K.E and P.E, (c) Sum of K.E and P.E, (d) Square root of K.E and P. E, , 4. What is true for quantum mechanics, , , , Dr. Pravin Kumar Singh, Assistant Professor, Physics Page 1

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(a) Vparticle = Wwave, (b) Vparticle < Vwave, (C) Vwave > Voparticle, (d) None, , 5. Which of the following statements about operators is, incorrect?, , (a) Any number can be used as an operator, , (b) Most operators in quantum mechanics are made, up of multiplication and differentiation, instructions, , (c) Operators act on the function written after them, , (d) Operators can be moved around in an expression, without altering the result, , 6. Which of the following statements about the properties, of operators consisting only of multiplication and, differentiation instructions is incorrect?, , (a) They all obey associativity, (b) They all commute, , (c) All these are correct, , (d) They are all linear, , , , Dr. Pravin Kumar Singh, , Assistant Professor, Physics Page 2

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7. The defintion of an observable is:, (a) The energy of a system, (b) The expectation value of an operator, (c) A dynamic variable that can be physically measured, , (d) Something you can see, , 8. What is the momentum epee, , ., OW a? p, (a) —ih— (b) x (c) -7£ (d) ~~ V(x), 9, The expectation value is the of the, observable, , (a) uncertainty, (b) variance, (c) mean value, , (d) most probable value, , 10. Which of the following pairs represent eigenfunctions, and corresponding eigenvalues of the differential, operator d/dx?, , , , Dr. Pravin Kumar Singh, Assistant Professor, Physics Page 3

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(a)e*,i (b)e*,2x (c) e* , 2x? (d) sinax,a, , 11. Which one of the following statements about Hermitian, operators is not correct?, , (a) All Hermitian operators represent observables, , (b) The eigenvalues of a Hermitian operator are real, , (c) All operators which represent observables are, Hermitian, , (d) The eigenfunctions of a Hermitian operator form a, , complete basis, , 12. The commutator of the operators A and B is defined, as, , (a) AB + BA, (b) AB + BA, (c) AB/BA, (d) AB- BA, , , , Dr. Pravin Kumar Singh, Assistant Professor, Physics Page 4