3.22 Use the above result to find the steady-state motion of a damped harmonic oscillator thatis driven by a periodic square-wave force of amplitude Fo. In particular, find the relativeamplitudes of the first three terms, A₁, A3, and A. of the response function x(t) in the casethat the third harmonic 30 of the driving frequency coincides with the frequency @ of theundamped oscillator. Let the quality factor Q = 100.

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Answered: 3.22 Use the above result to find the…

Physical Chemistry

2nd Edition

ISBN:9781133958437

Author:Ball, David W. (david Warren), BAER, Tomas

Publisher:Ball, David W. (david Warren), BAER, Tomas

Chapter10: Introduction To Quantum Mechanics

Section: Chapter Questions

Problem 10.26E: For a particle in a state having the wavefunction =2asinxa in the range x=0toa, what is the...

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For a particle in a state having the wavefunction =2asinxa in the range x=0toa, what is the probability that the particle exists in the following intervals? a x=0to0.02ab x=0.24ato0.26a c x=0.49ato0.51ad x=0.74ato0.76a e x=0.98ato1.00a Plot the probabilities versus x. What does your plot illustrate about the probability?
For a particle in one-dimensional box of length a, w, = ax(a – x) and w2 = x(a – x)(a + x) can each be also as an approximate solutions. (i) How large is then the underestimation in ground state energy (in %) using these 1/2 W1 or wz as compared to the exact solution using w = (2/a)""sin(nnx/a). (ii) Which of them (w, or w2) give a closer estimation of the energy?
For a system rotating in three dimensions. what is the degeneracy of the level with I=4? What are the valid values of m,?
Consider the following two systems: (a) an electron in a onedimensional box of length 1.0 Å and (b) a helium atom in acube 30 cm on an edge. Calculate the energy differencebetween ground state and first excited state, expressing youranswer in kJ mol-1.
A one-particle, one-dimensional system has the state function Y = (sinat) (2)+(cosat) (32) 14 2-x² / c² xe where a is a constant and c = 2.000 Å. If the particle's position is measured at t = 0, estimate the probability that the result will lie between 2.000 Å and 2.001 Å.
4.8 Show that the rotational frequency spectrum of a diatomic molecule will consist of equally spaced lines separated by an amount Av=h/4n°I, where I is the moment of inertia of the molecule.
A one-particle, one-dimensional system has the potential energy function V = V₁ for 0 ≤ x ≤ 1 and V = co elsewhere (where V, is a constant). a) Use the variation function = sin() for 0 ≤ x ≤ 1 and 0 elsewhere to estimate the ground-state energy of this system. b) Calculate the % relative error.
19) Describe requirements for the well-behaved wavefunction.
Calculate the probability that a ClO molecule treated as a harmonic oscillator will be found at a classically forbidden extension or compression when v=3.
Assuming the antenna of a 10.0-kW radio station radiates spherical electromagnetic waves, (a) compute the maximum value of the magnetic field 5.00 km from the antenna and (b) state how this value compares with the surface magnetic field of the Earth.
A 1.00 kg weight is traveling at a constant velocity of 10.0 ms-1, in a cubic room 3.00 m on an edge.(a). Determine the sum of the squares of its three quantum numbers.(b). What would be the ground state energy for this weight?
Q1: Find the first excited state of harmonic oscillator using the equation: . (x) = A, (a.)"V(x), with E, (n+hw Q2: If f and T are the position and Kinetic energy operators, respectively. Where: Calculate [f ,T]. 2m ax

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