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# INTRO QUANT MECH 1 PHY 4604

UF

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This 2 page Study Guide was uploaded by Mrs. Linda Wiegand on Friday September 18, 2015. The Study Guide belongs to PHY 4604 at University of Florida taught by Staff in Fall. Since its upload, it has received 21 views. For similar materials see /class/206768/phy-4604-university-of-florida in Physics 2 at University of Florida.

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Date Created: 09/18/15

Study GuidePractice Exam 1 PHY 4604 Fall 2003 This practice exam is almost the same as the Fall 2002 one which you can nd on last year s web site Rather than look at the solution to that practice exam right away I suggest that you try to do this on your own rst You are likely to learn more that way Last year s web site also contains the actual rst exam and its solution There are four parts to the exam a short answer section in which I will choose ve of the questions from part 1 below a section on expectation values and the uncertainty principle a section on the expansion hypothesis in the context of a particle in a box and a section on one dimensional potentials On the actual exam I will try to choose problems which can be done in the alloted time 50 minutes Remember you are not allowed any formula sheets or a calculator on the exam 1 Short answer section I What is Planck s constant numerically What is the timedependent Schrodinger equation What is the timeindependent Schrodinger equation What is the continuity equation What is the probability current in one dimension Let be a wave function on the interval 700 lt x lt 0 Give expressions for the expectation value of x and p What is the Fourier transform of in kspace see Class 8 Give expressions for the expectation values of x and p using see Class 8 Given how does one go back and determine see Class 8 What is the normalization condition for What is the normalization condition for 1M see Glass 8 What is the uncertainty principle What is the condition for a set of wave functions u x to be orthonormal A set of wave functions u x for n 12 3 i i on the interval 11 is said to be complete or satisfy the expansion hypothesis What does this mean In a region where the potential is constant Vx V0 what is the form of the solution to the timeindependent Schrodinger equation if E gt V0 What is the form if E lt V0 For a piecewise constant potential in one dimension what are the boundary conditions for the wave function at a step in the potential What are the boundary conditions for a wave function at a delta function potential 2 The ground state of a particle in a box between 0 lt x lt a is C sin7rxai Determine the constant C from the normalization condition What is the expectation value of x Hint you can determine this by symmetry What is Ax Here you will have to do an integral On the exam if you can not do an integral but set up the integral correctly you will get partial credit What is the expectation value of the momentum What is Ap Compare your results with A95 and Ap to the uncertainty principle 3 Consider the wave functions CW sinn7rxa on the interval 0 lt x lt 1 a Show that these wave functions are orthogonal b Determine the normalization constants Cw c These wave functions are complete on the interval 0 lt x lt 1 Let 1 for 0 lt x lt 0511 and 0 otherwise Express as a sum of the form x 2mm 1 You need to determine the coefficients A tb Consider the potential in one dimension Vx 0 for x lt 0 Vx V0 for x gt 0 and Vx h22ma6x at x 0 Suppose E gt Vol a What is the form of the solution to the timeindependent Schrodinger equation for x lt 0 b What is the form of the solution to the timeindependent Schrodinger equation for x gt 0 c What are the boundary conditions at x 0 d Solve for the wave function for a wave coming from the right e Determine the transmission and re ection probabilities ls probability conserved

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