4.9 A particle is trapped inside an infinite one-dimensional square wellof width a in the first excited state (n = 2).(a) You make a measurement to locate the particle. At what po-sitions are you most likely to find the particle? At what positionsare you least likely to find it?(b) Calculate (p2) for this particle.

Answered: 4.9 A particle is trapped inside an…

University Physics Volume 3

17th Edition

ISBN:9781938168185

Author:William Moebs, Jeff Sanny

Publisher:William Moebs, Jeff Sanny

Chapter8: Atomic Structure

Section: Chapter Questions

Problem 67P: What is the minimum frequency of a photon required to ionize: (a) a He+ ion in its ground stare? (b)...

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A particle in an infinite well is in the ground state with energy1.54eV. How much energy must be added to the particle to reach the second excited state (n = 3)? The third excited state (n = 4)?
PROBLEM 3. Using the variational method, calculate the ground state en- ergy Eo of a particle in the triangular potential: U(r) = 0 r 0. Use the trial function v(x) = Cx exp(-ar), where a is a variational parameter and C is a normalization constant to be found. Compare your result for Eo with the exact solution, Eo 1.856(h? F/m)/3.
What is the minimum frequency of a photon required to ionize: (a) a He+ ion in its ground stare? (b) A Li2+ ion in its first excited state?
PROBLEM 2. Consider a spherical potential well of radius R and depth Uo, so that the potential is U(r) = -Uo at r R. Calculate the minimum value of Uc for which the well can trap a particle with l = 0. This means that SE at Uo > Uc has at least one bound ground state at l = 0 and E < 0. At Ug = Uc the bound state disappears.
6QM Please answer question throughly and detailed.
A particle of mass m is contained in a one-dimensional infinite well extending from L to x=- 2 L The particle is in its ground state given by ø.(x)= /2/L cos(zx/L). X = - The walls of the box are moved suddenly to form a box extending from x = -L to x= L. what is the probability that the particle will be in the ground state after this sudden expansion?
Consider a particle of mass m, located in a potential energy well.one-dimensional (box) with infinite height walls. The wave function that describes this system is:Ψn(x) = K sin (nπx /L), for 0 ≤ x ≤ LΨn(x) = 0 for any other value.K is a constant and n = 1,2,3,... Determine K*K = │K│2
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Imagine we model a proton inside an atom’s nucleus as if it were a particle in a one-dimensional box. In this case, the width of the box should be approximately 10 fm. What are the energies of the proton for the ground state, first excited, and second excited state? If the proton dropped from the first excited or second excited to the groud state by emitting a photon, what energy would the photon carry in each case?
Suppose a harmonic oscillator is subject to a perturbation av = Ahw (&/#0)* . where ro = mw/h is the length scale of the problem. a) Use Rayleigh-Schrödinger perturbation theory to find the first and second order corrections to the energies of the n'th level. b) Discuss the applicability of the perturbative approach for states with large n,
Evaluate the E expressions for both the Classical (continuous, involves integration) and the Quantum (discrete, involves summation) models for the energy density u, (v).

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