Thermodynamics, Statistical Physics, and Quantum Mechanics

56 5.11 Square Well (MIT) A particle of mass isconfined to a space in one dimension by infinitelyhigh walls at At the particle i ...

57 At time the particle’s wavefunction is given by The constant is unrelated to any otherparameters. What is the proba- bility t ...

58 and define the operators a) Suppose wedefine a state to obey Showthat thestates are eigenstates of thenumber operator, with e ...

59 where is theexacteigenstate of the harmonicoscillatorwitheigen- value a) Give b) What is the parity of this state? Does it ch ...

60 b) What is theeigenvalue of theground state? c)At time anelectric field isswitched on,adding aperturba- d) Assuming that the ...

61 5.24 Triplet Square Well (Stony Brook) Consider atwo-electronsystem inonedimension, whereboth electrons have spins aligned in ...

62 5.27 Three Spins (Stony Brook) Considerthree particles of spin 1/2 which have no motion. The raising and lowering operators o ...

63 At the system is instate Derive the probabilitythat at any later time it is in state 5.29 Rotating Spin (Maryland, MIT) A spi ...

64 5.33 Linear Potential II (MIT, Tennessee) A particle ofmass moves in onedimension inthe righthalf-space. It has a potential e ...

65 a) Using the normalized trialfunction find the value of which minimizes the ground stateenergy and the resulting estimate of ...

66 Assume a wave function of the form where is the Bohr radius, is the variational parameter, and is the spin state of the two e ...

67 where is theangle around the circle. Anelectric field is imposed in the plane of the circle. Find theperturbedenergylevels up ...

68 The same small constantUoccurs inbothterms of Useperturbation theory tocalculate thechange in theground stateenergy to order ...

69 What are the eigenvalues of thegroundstate and the lowestexcited states ofthe three-dimensionalharmonicoscillator? Use pertur ...

70 Then weimpose twosimultaneousperturbations: anelectric field in the and a magneticfield which is given by the vectorpotential ...

71 WKB 5.53 Bouncing Ball (Moscow Phys-Tech, Chicago) A ball ofmass acted on byuniformgravity (let be theacceleration of gravity ...

72 5.56 Ramp Potential (Tennessee) Use WKB in one dimension to find theeigenvalues of aparticle ofmass in thepotential where 5.5 ...

73 5.58 Ramp Phase Shift (Tennessee) Use WKB to calculate the phase shift in one dimension of aparticle of mass confined by ther ...

74 5.62 Step-Up Potential (Wisconsin-Madison) Consider aparticlescattering in one dimension from a potential which is a simple s ...

75 5.63 Repulsive Square Well (Colorado) Consider inthreedimensions a repulsive squarewell at theorigin of width Thepotential is ...