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Pune University - Sem - I : Quantum Mechanics - I, April 2010

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Total No. of Questions : 7] [Total No. of Pages : 3 P883 [3722]-104 M. Sc. PHYSICS PHY UTN - 504 : Quantum Mechanics - I (New Course) (Sem. - I) Time : 3 Hours] [Max. Marks : 80 Instructions to the candidates : 1) Question No. 1 is compulsory. 2) Attempt any four from the remaining. 3) Figures to the right indicate full marks. 4) Draw neat diagrams wherever necessary. 5) Use of Mathematical tables and pocket calculator is allowed. Q1) Attempt any four of the following : a) [16] The spectral density of a matter wave-packet is in the form of a symmetrical exponential as : (k) = Ae | k | Find the form of wave function (x). b) The x-component of a linear momentum Px is classically expressed as Px = m dx . By using Schroedinger equation, show that dt + Px = c) * i x (x, t ) ! (x, t ) dx . Define : i) adjoint of an operator A ii) Hermitian operator and () + Show that A B = B+ A + d) Explain unitary operator. Show that the norm of a state functions do not changes under unitary transformation. P.T.O.

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Additional Info : M.Sc. PHYSICS, PHY UTN - 504 : Quantum Mechanics - I (New Course) (Semister - I), Pune University
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