Consider the wave function for the ground state harmonic oscillator:1/4&(x) = (mw)¹⁄ª e−m w x²/(2 h)A. Evaluate the integral: dxsymbolic formatting help Consider the harmonic oscillator wave function:-0.4psir0.0 0.2 0.4 0.6т-4-202xaxisA. What is the quantum number for this state? v = 4B. If w = 47.25 ×1015 s-1 evaluate Ĥ₁ =

All parts are solved below.Explanation:

Answered: Consider the wave function for 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 1 Consider a 1d oscillator subject to an additional constant force F, so that the potential energy is given by: mw? -x² – Fx 2 U (x) = | Using the solution of the SE for oscillator at F = 0, write down the wave functions and the energy levels at F > 0. Can the ground state energy of ocillator under a constant force be negative? HINT: The force F causes a displacement of U(x) without changing its parabolic shape.
A ID harmonic oscillator of angular frequency w and charge q is in its ground state at time t=0. A perturbation H'(t) = qE eA3 (where E is ekctric field and ß is a constant) is %3D applied for a time t = t. Cakulate the probability of transition to the first and second excited state. (hint: you may expand exponential in perturbation and keep it only up to linear term)
What is the energy level difference between adjacent levels ∆En = En +1 - En for the simple harmonic oscillator? What are ∆E0, ∆E2, and ∆E20? How many possible energy levels are there?
How.: Normalize a wafct. for a particke at leny th L given by: Y x) z x (L-x). in a box
Legrende polynomials The amplitude of a stray wave is defined by: SO) =x (21+ 1) exp li8,] sen 8, P(cos 8). INO Here e is the scattering angle, / is the angular momentum and 6, is the phase shift produced by the central potential that performs the scattering. The total cross section is: Show that: 'É4+ 1)sen² 8, .
Find the locations where the probability density has its maximum values for the wave function w(x) = A(2ax² - 1)e-ax2/2, which represents the second excited state of the simple harmonic oscillator. I
Find the normalization constant B for the combination 18. As noted in Exercise 8, a linear combination of two wave functions for the same sysstem is also a valid wave function also a valid wave function functions for the same system 2TX = B sin TX +sin L. L. of the wave functions for then = 1 and n = 2 states od %3D particle in a box L wide. [A + CO]
Use the ground-state wave function of the simple har- monic oscillator to find x, (x²), and Ax. Use the nor- malization constant A = (mw0/hr)1/4. av ay
Prove that (x) = 0 for the ground state of a harmonic oscillator. b) Prove that (2²) 2 uk for the ground state of a harmonic oscillator. c) Use the result in (b) to calculate the root-mean-square amplitude of 1ªN2 in its ground state. Use k = 2260 N m-1 for 14N2. The mass of 14N = 14.003 amu. d) The value you obtained in (c) is a measure of how much the bond length in this molecule varies (about its equilibrium length) due to vibrational motion. Given that the equilibrium bond length of 14N2 is 109.77 pm, by how much does the bond length vary due to vibrational motion, as a percent of its equilibrium value?
om CourseHero.com on 03 3. The first excited state of the harmonic oscillator is given by the one-dimension wave function ₁(x) = (4x³/π)¹/4 x e-ax²/2. (a) Find the average value of the kinetic energy (K) for this wave function. (b) How does (K) compare to the total average energy (E) for ₁? Show all math.
Q.3 a) Which type of molecules exhibit infra-red spectra? Calculate the vibrational energy and force constant of 'H"F if its vibrational frequency is 3.0 x 1014 Hz. b) Prove that the eigenvalues of a Hermitian operator are real.
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