68110976-Midterm-2-Solutions

# 68110976-Midterm-2-Solutions - Section A December 30, 2010...

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Section A December 30, 2010 EP 341 Quantum Physics Exam-2; Time Interval: 17:00-18:30 Name Surname: ID No: Lecturer: Prof. Dr. Ramazan Koç 01 02 03 04 05 06 Total Question 1. Match the observable/quantity/system with the operator, eigenfunctions, eigenvalues and other relations . Observable/System/Quantity Operator eigenfunction eigenvalues Other (briefly explain) Momentum l b j Harmonic Oscillator (1D) z d h Harmonic Oscillator(Spherical) q D w Potential Barrier B,F m i(potential barrier) s(def’n of wave vec) Finite Potential well B,F o e g(potential well) s(def’n of wave vec) Step Potential B,F c a(step potential) s(def’n of wave vec) Spherical Potential well k f p Ring Potential t u v Time dependent Schr. equation x Infinite potential well B E y Angular Momentum A r n (a) (b) (c) (d) (e) (f) (g) (h) (i) (j) (k) (l) (m) (n) (o) (p) (q) (r) (s) (t) (u) (v) (x) (y) (z) (w) (A) (B) (D) (E) (F)

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Section A December 30, 2010 Question 2. Answer the following questions on the postulates of quantum mechanics. a) 1st postulates of quantum mechanics state that “ Each physical system is described by a wave function which determines all can be known about the system.” What are the fundamental behaviors of the wave function? b) How can you determine wave function of a quantum particle?(2nd postulate) c) What is the meaning of correspondence principle? d) What is the expectation value and eigenvalue of an operator? When they are the same? e) How can you determine location of a particle? What is the meaning of normalization and orthogonalization? Answer 2: a) Fundamental behaviors of the wave function A wave function must be Single valued: A single-valued function is function that, for each point in the domain, has a unique value in the range. Continuous: The function has finite value at any point in the given space.
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## 68110976-Midterm-2-Solutions - Section A December 30, 2010...

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