Question A3Consider 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 energylevels.Add to your sketch the form of the wavefunction and the probability density in the threelowest energy states.[10 marks]

Answered: Image /qna-images/answer/df7c6738-8bf1-42de-8ae3-c8e7d7ac9e9f.jpg

Answered: Question A3 Consider the energy…

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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There is an electron, in a 1-d, infinitely deep square potential well with a width of d. If it is in ground state, 1. Draw the electron's wavefunction. Show the position of the walls of the potential well. 2. Explain how the probability distribution for detecting the electron at a given position differs from the wavefunction.
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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?
Consider the following wave function. TT X a = B sin(- (x) = E 2 π.χ. a −) + C · sin(² a. Does this function describes a particle-in-a-box acceptable wave function? Name the conditions to be fulfilled. b. Is this function an eigenfunction of the total energy operator H when H is the Hamilton operator.
Below is a figure that depicts the potential energy of an electron (a finite square well), as well as the energies associated with the first two wave-functions. a) Sketch the first two stationary wavefunctions (solutions to the Schrődinger equation) for an electron trapped in this fashion. Pay attention to detail! Use the two dashed lines as x-axes. U(x) E2 E1 b) If the potential energy were an infinite square well (not finite well as shown above), what would the energy of the first two allowed energy levels be (i.e., E1 and E2). Write the expressions in terms of constants and a (the width of the wellI) and then evaluate numerically for a = 6.0*1010 m. [If you don't remember the formula, you can derive it by using E = h²k²/2m, together with the condition on À = 2a/n.] c) Let's say I adjust the width of the well, a, such that E1 = 3.5 ev. In that case, calculate the wavelength (in nanometers) of a photon that would be emitted in the electron's transition from E2 to E1. [Remember: hc =…
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B3
Y:0. 4 %YO N Derive an equation which is represent the time-dependent Schrödinger equation. * 1 Add file This is a required question If Å is the position operator, and P, is the linear momentum operator, solve the following commutative, [X² ,P.] =?. 1 Add file If the operator Â = 3 in , and the wave function Y = 8 e-4ix , find the eigenvalue of (Â¥),Is ¥ an eigen function of the operator Â? dx 1 Add file Page 4 of 5 Вack Next Never submit passwords through Google Forms. العربية الإنجليزية
I need help with these problems. I don't know how to approach them. I want see detailed steps.
Please solve quickly
1.The odd parity eigenstates of the infinte square well , with potential V = 0 in the range −L/2 ≤ ? ≤ L/2, are given by : (see figure) and have Ψn(x, t) = 0 elsewhere , for n=2 , 4 , 6 etc a) Sketch the potential of this system , including in your sketch the positions of the lowest three energy levels . Indicate in your sketch the form of the wavefunction for a particle in each of these energy levels , and state which of the wavefunctions you have drawn could be decirbed by the Ψn written above (see figure) . b) Calculate the expectation value of momentum , ⟨p⟩ for a particle with n=2 c) Calculate the expectation value of momentum squared ⟨p 2⟩ , for a particle with n = 2 . Hint : you may use the mathematical identiy sin2 x = 1/2 (1 − cos 2x) without proof .

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