A particle, which is initially (t = 0) in the ground state of an infinite, one-dimensional potential box with walls at x = 0 and x = a, is subjected for 0 < t s∞, to a perturbation V (t) = x*e. Calculate to first order the probability of finding the particle in its first excited state for t>0.

A particle, which is initially (t = 0) in the ground state of an infinite, one-dimensional potential box with walls at x = 0 and x = a, is subjected for 0 < t s∞, to a perturbation V (t) = x*e. Calculate to first order the probability of finding the particle in its first excited state for t>0.

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)...

See similar textbooks

Related questions

Q: For a particle that exists in a state described by the wavefunction Ψ(t, x), imagine you are…

Q: What are the energy eigenvalues for a particle that has mass m and is confined inside of a…

A: We are given mass of particle. We are also given that particle in in 3D box. Its length along x…

Q: P2. Consider the motion of a particle of mass m moving in a 3-d potential, V(x, y, x) = k(x2 + y2 +…

Q: What is the energy of a particle restricted by an infinite square well and move along the interval 0…

A: In the infinite square well potential we have wavefunction and energy in the interval…

Q: Consider a particle in the infinite potential well at -a <I < a. The particle is in a superposition…

A: The given wave function and its complex conjugate be defined as,…

Q: an insulatung spiere radius T O centimeters irge coulombs Is distri Volume the insulating spn…

A: Given that:- Radius of insulating sphere=R=10cm

Q: For sinusoidal perturbation, H'(F,1)=VF)cos(x), show that the transition probability is given by…

A: Basic Details The perturbation is the deviation of a moving object form the regular state caused by…

Q: For the infinite square-well potential, fi nd the probability that a particle in its ground state is…

A: Given information: An infinite square-well potential. We have to find the probability that a…

Q: Consider the first excited state of the quantum harmonic oscillator (v = 1) and the wavefunction…

A: For quantum harmonic oscillator, its position extends from..For a wave function to be normalized,…

Q: Calculate the uncertainties dr = V(r2) and dp = Vp?) for a particle confined in the region -a a, r…

A: As we can see the given wave function is normalised and in outside region it's zero. Therefore This…

Q: As a 1-dimensional problem, you are given a particle of mass, m, confined to a box of width, L. The…

Q: Calculate the period of oscillation of ?(x,t) for a particle of mass 1.67 × 10-27 kg in the first…

A: Given: m=1.67×10-27kg, a=1.68×10-15m The energy of a particle in a box of width a is defined by :…

Q: A quantum system is composed of an electron in free movement in a region one- dimensional, between O…

A: Solving the Schrodinger equation for any kind of potential is a hard thing to do. In most cases, we…

Q: For the nth stationary state of the harmonic oscillator, using the algebraic method, show that: = (…

Q: provided that a particle is described by the normalized wavefunction ψ(x)=(2a/π)1/4e-ax^2 with…

Q: An atom with total energy 1.84 eV, in a region with no potential energy, is incident on a barrier…

Q: A particle with mass m is moving along the x-axis in a potential given by the potential energy…

A: The potential energy function U(x)=0.5mω2x2 describes a simple harmonic oscillator in quantum…

Q: Calculate the period of oscillation of Ψ(x) for a particle of mass 1.67 x 10^-27 kg in the first…

Q: theory

Q: if the particle has the wavelenght si =a*x^2 between x = 0 and si =0 elsewhere. find the probability…

Q: A particle with the energy E is incident from the left on a potential step of height Uo and a…

A: This problem is a combination of step and delta function. There are two regions here, one is x<0,…

Q: A system is in an eigenstate |m, l) of the angular momentum operators L2 and L2. Calculate the…

Q: A particle of mass m moves non-relativistically in one dimension in a potential given by V(x) =…

Q: Consider a particle with the following wave-function: ,xL and L and A are constants. (a) What is the…

Q: Prove that the free energy of a semi-classical ideal gas is given by the following relationship F =…

Q: - Consider a particle of mass m confined in a one-dimensional infinite square well of width a. The…

Q: Consider a classical particle of mass m moving in one spatial dimension with position x and momentum…

Q: An electron possessing the kinetic energy E approaches a potential barrier of the height U = 2E and…

A: Given data, Kinetic energy of the incident electron = E Potential energy of the barrier U = 2E

Q: A particle is confined to a 1D box between x=0 and x=1 and has the normalized wavefunction of 105 V…

Q: Show that is a solution to the time-independent Schrödinger equation, with potential V(x) = 2h²² and…

A: Given: The potential of the particle is Vx = 2 ħ2 m x2 The energy Eigenvalue of the particle is E =…

Q: b1 (x) = A sin () L

Q: If you have a system with two levels of energy. Prove that the probabilities of absorption and…

Q: Suppose you have a "box" in which each particle may occupy any of 10 single-particle states. For…

A: Each particle may occupy any of 10 single-particle states, each with zero energy. Er1=0 for 1≤i≤10…

Q: Consider a particle of mass m moving in one dimension with wavefunction $(x) Vi for sin L - and zero…

A: The momentum operator is given by Therefore the operator is given by Where The given wave…

Q: Suppose you have a "box" in which each particle may occupy any of 10 single-particle states. For…

A: Given that we have a "box" in which each particle may occupy any of 10 single-particle states. For…

Q: The classical turning points of a harmonic oscillator occur at the displacements at which all of the…

A: The energy of the oscillatoe for state ν=0 is given byNow equating this energy with potential…

Q: 25. Consider a particle of mass m in a one-dimensional infinite square well with V (x) = 0 for 0 ≤ x…

A: We are asked to calculate the probability that a particle starting in the ground state will…

Q: The perturbation [b(a-x) H'= -a <x <a otherwise acts on a particle ofmass 'm' confined in an…

A: Solution attached in the photo

Q: Let y, (x) denote the orthonormal stationary states of a system corresponding to the energy En.…

A: Expectation value of energy

Q: Use the time-dependent Schroedinger equation to calculate the period (in seconds) of the…

A: Mass of particle m = 9.109 × 10− 31 kg Width of the box a = 1.2 ×10− 10 m

Q: S-U. 10. -U, -c<r <c %3D otherwise

A: Given wave function as, ψ(x)=a(b+x);-b<x<0a(b-x);0<x<b0;otherwise

Q: v (z, t) is a solution of the Schrödinger equation for a free particle of mass m in one dimension,…

Q: Suppose we had a classical particle in a frictionless box, bouncing back and forth at constant…

Concept explainers

Connection formulae for WKB approximation

In quantum mechanics, Schrödinger’s equation for certain systems with varying parameters cannot be solved directly. In such a case, an approximation method is used to obtain the approximate solution. WKB method is a special technique used to obtain the approximate solution for Schrödinger’s time-independent equation. In general, the WKB method is used to solve linear differential equations with varying coefficients. This method is called semiclassical approximation in quantum mechanics.

Question

100%

A particle, which is initially (t = 0) in the ground state of an infinite, one-dimensional
potential box with walls at x = 0 and x = a, is subjected for 0 <t < ∞, to a perturbation
V (t) = x'e. Calculate to first order the probability of finding the particle in its first excited
state for t >0.

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

Step 2

Step 3

Step 4

Step 5

Trending now

This is a popular solution!

Step by step

Solved in 5 steps with 5 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

Connection Formulae for WKB approximation

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, physics and related others by exploring similar questions and additional content below.

Similar questions

Calculate the uncertainties dr = V(x2) and op = V(p²) for %3D a particle confined in the region -a a, r<-a. %3D
A particle with mass m is in the state mx +iat 2h V (x, t) = Ae where A and a are positive real constants. Calculate the expectation value of (p).
Determine the probability distribution function in the phase space for a relativistic particle in a volume V and with energy ε(p) = √√√/m²c²+p²c², where p is the ab- solute value of the momentum, m the mass, and c the speed of light. Give the final result in terms of the modified Bessel functions r+∞ Ky (z) = ™ (v-1)! 2 -zcosht e cosh (vt) dt Ky(z) ~ Check what happens in the limit ² →0. mc² kT z 0.
When a particle of energy E approaches a potential barrier of height V0, where E >> V0, show that the refl ection coeffcient is about {[V0 sin(kL)]/2E} 2
Evaluate the E expressions for both the Classical (continuous, involves integration) and the Quantum (discrete, involves summation) models for the energy density u, (v).
Suppose that in a certain system a particle free to move along one dimension (with 0 ≤ x ≤ ∞) is described by the unnormalized wavefunction Ψ(x)=e-ax with a = 2 m−1. What is the probability of finding the particle at a distance x ≥ 1 m?
Consider the wavefunction Y(x) = exp(-2a|x|). a) Normalize the above wavefunction. b) Sketch the probability density of the above wavefunction. c) What is the probability of finding the particle in the range 0 < x s 1/a ?
Consider the one-dimensional step-potential V (x) = {0 , x < 0; V0 , x > 0}(a) Calculate the probability R that an incoming particle propagating from the x < 0 region to the right will reflect from the step.(b) Calculate the probability T that the particle will be transmitted across the step.(c) Discuss the dependence of R and T on the energy E of the particle, and show that always R+T = 1.[Hints: Use the expression J = (-i*hbar / 2m)*(ψ*(x)ψ′(x) − ψ*'(x)ψ(x)) for the particle current to define current carried by the incoming wave Ji, reflected wave Jr, and transmitted wave Jt across the step.For a simple plane wave ψ(x) = eikx, the current J = hbar*k/m = p/m = v equals the classical particle velocity v. The reflection probability is R = |Jr/Ji|, and the transmission probability is T = |Jt/Ji|. You need to write and solve the Schrodinger equation in regions x < 0 and x > 0 separately, and connect the solutions via boundary conditions at x = 0 (ψ(x) and ψ′(x) must be…
3
Calculate the average or expectation value of the position of a particle in a one-dimensional box for n=2.
If the Hamiltonian of the one-dimensional classical harmonic oscillator is given by H(p2/2m) +(½)mw? x², this oscillator's a) the partition function b) Helmholtz free energy cc) Average energy
consider an infinite square well with sides at x= -L/2 and x = L/2 (centered at the origin). Then the potential energy is 0 for [x] L/2 Let E be the total energy of the particle. =0 (a) Solve the one-dimensional time-independent Schrodinger equation to find y(x) in each region. (b) Apply the boundary condition that must be continuous. (c) Apply the normalization condition. (d) Find the allowed values of E. (e) Sketch w(x) for the three lowest energy states. (f) Compare your results for (d) and (e) to the infinite square well (with sides at x=0 and x=L)