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Unformatted text preview: Quantum I (PHYS 3220) concept questions Schrdinger Equation Consider the eigenvalue equation How many of the following give an eigenfunction and corresponding eigenvalue? I. f(x) = sin(kx), C = +k 2 II. f(x) = exp(x), C = +1 III. f(x) = exp(i k x), C = k 2 IV. f(x) = x 3 , C = 6 A) 1 B) 2 C) 3 D) all 4 E) None ) ( )] ( [ 2 2 x f C x f dx d = 31 Is ? d dt * ( x , t ) ( x , t ) dx = d dt * ( x , t ) ( x , t ) ( 29 dx A)Yes, no problem! B)Theres something not right about this Two particles, 1 and 2, are described by plane wave of the form exp[i(kxt)]. Particle 1 has a smaller wavelength than particle 2: 1 < 2 Which particle has larger momentum? A)particle 1 B) particle 2 C) They have the same momentum D)It is impossible to answer based on the info given. 36 1 (x, t) and 2 (x, t) are two solutions of the timedependent SE. Is sum (x, t) = a 1 (x, t) + b 1 (x, t) also a solution of the TDSE? A) Yes, always B) No, never C) Depends on 1 (x, t) and 2 (x, t) D) Depends on a and b 32 1 (x, t) and 2 (x, t) are two NORMALIZED solutions of the time dependent SE. Is sum (x, t) = a 1 (x, t) + b 1 (x, t) also a normalized solution of the TDSE? A) Yes, always B) No, never C) Depends on 1 (x, t) and 2 (x, t) D) Depends on a and b 32 Which expression below would be the QM equation for <KE>? A) B) C) D) None of these! E) More than one! ( 29 x t x t x m k d ) , ( ) , ( 2 * 2 2   ( 29 x t x x t x m d ) , ( ) , ( 2 2 2 * 2   ( 29 x t x t x x m d ) , ( ) , ( 2 * 2 2 2   After assuming a product form solution (x,t) = (x) (t), the TDSE becomes If the potential energy function V in the Schrdinger Equation is a function of time, as well as x [V = V(x,t)] would separation of variables still work; that is, would there still be solutions to the SE of the form (x,t) = (x) (t)? A) Yes, always B) No, never C) Depends on the functional dependence of V on x and t E V x m t i = + = 2 2 2 1 2 1 30 1 (x, t) and 2 (x, t) are two solutions of the timedependent SE. Is sum (x, t) = a 1 (x, t) + b 2 (x, t) also a solution of the TDSE? A) Yes B) No C) Depends on 1 (x, t) and 2 (x, t) D) Depends on a and b 32 Do you know what the momentum operator is? A) Yes B) No 33 Do you plan to attend todays Tutorial (on relating classical to Quantum, and qualitative sketching of wave functions) A) Yes, at 3 pm B) Yes, at 4 pm C) Perhaps, more likely at 3 D) Perhaps, more likely at 4 E) No, cant come/not planning on it. Given n (x, t) as one of the eigenstates of n = E n n , what is the expectation value of the Hamiltoniansquared?...
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This note was uploaded on 02/27/2012 for the course PHYSICS 3220 taught by Professor Stevepollock during the Fall '08 term at Colorado.
 Fall '08
 STEVEPOLLOCK

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