Question A3A wavefunction takes the form = A sin(2x) in the interval -1 < x < 1, and is zero everywhereelse. You may take A to be a real-valued constant.a) Calculate the value of the constant A by performing a normalization.b) Calculate the probability of finding this particle in the region 0 < x < 1/16.[8 marks]

Step 1: Step 2: Step 3: Step 4:

Answered: Question A3 A wavefunction takes the…

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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Problem Consider the ODE x = 2-3x with initial condition x(to) = 1 and to = 0. What is the value of the state x when t = 2? Estimate when the system will decay to a constant value using the time constant of the system (i.e., after 4 time constants)? 4
Solve the question below completely mentioning each and every step
please solve number 4
Part A Which particle can have its velocity known most precisely? Match the words in the left column to the appropriate blanks in the sentences on the right. Reset Help smallest position uncertainty The particle with the most precisely known velocity has the This can be observed for and the greatest wave function amplitude. smallest position uncertainty and wave function amplitude. greatest position uncertainty. The wave function amplitude does not play a role. greatest position uncertainty and the smallest wave function amplitude. Figure (x) (x) particle 1. AAAAA particle 2. particle 3. Particle 1 Particle 2 (x) particles 2 and 3. particles 1 and 2. Particle 3 Submit Previous Answers Request Answer
Question 3 Consider the simple and close-packed hexagonal direct lattices. (a) Find out the general expression for the structure factor for each lattice type. In this context, what is the significance of a complex structure factor? (b) Without resorting to the structure factor, determine in which structure(s) X-ray Bragg reflections arise from the lattice planes (0001), (0002), and (1010). Justify your answer by the use of the above determined structure factor or otherwise and explain the meaning of the four indices describing the above cited lattice planes.
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We will consider the Schrödinger equation in this problem as well as the analogies between the wavefunction and how boundary conditions are an essential part of developing this equation for various problems (situations). a) Write the form of the time-independent Schrödinger equation if the potential is that of a spring with spring constant k. Write the form of the time-dependent Schrödinger equation with the same potential. Briefly describe all the terms and variables in these equations. b) One solution to the time independent Schrödinger equation has the form Asin(kx). Why might it be called the wavefunction? If this form represents a wave of light, what is the energy for one photon? (Notek here stands for the wavevector and not the spring constant.) c) Why must all wavefunctions go to zero at infinite distance from the center of the coordinate system in all systems where the potential energy is always finite?
Question A3 Consider the energy eigenstates of a particle in a quantum harmonic oscillator with frequency w. a) Write down expressions for the energies of the three lowest states. b) c) Sketch the potential for this system, along with the position of the three lowest energy levels. Add to your sketch the form of the wavefunction and the probability density in the three lowest energy states. [10 marks]
1
Question A4 A particle is in an energy eigenstate described by the wavefunction (x,t) = v(x) exp(-iot/2), where σ is a constant. a) Apply the energy operator, Ê, to determine the energy eigenvalue of this particle. b) Show that the uncertainty in its energy, AE, is zero. [8 marks]
PLS CONTINUE THE ANSWER AND ANSWER D, E AND F HANDWRITTEN THEN BOX THE FINAL ANSWERS
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