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: -A system is defined by the wavefunction: 27nx (x) = A cos for 4 (a) Determine the normalization…

Q: An electron beam having energy 2 eV incidents on a potential barrier having width 20x10 10 m and…

A: When a particle of energy E is less than a potential barrier of height U, then the transmission…

Q: Consider an electron of energy 1 eV that encounters a potential barrier of width 0.1nm and energy…

Q: Calculate the energy of the nth excited state of a particle in a 1D box with hard walls at x = 0 and…

Q: A particle is confined to the one-dimensional infinite potential well of If the particle is in its…

Q: For a system of particles of mass m in the state p the formula expression for the particle flux…

A: Given that :F=h4πimΨ* ∂Ψ∂x-Ψ∂Ψ*∂xNow, as we know that the wavefunction of a free particle…

Q: Consider a state of total angular momentum I = 2. What are the eigenvalues of the operators (a) L, 3…

Q: Assembly consists of 8 classical systems distributed over five power strips of one cell, and their…

Q: The Boltzmann distribution - not valid when the number of available states is small - may result in…

A: Two casses are given, for that we have to expalin reason wise

Q: An electron is trapped in a finite potential well that is deep enough to allow the electron to exist…

Q: Is the ground-state energy of a proton trapped in a onedimensional infinite potential well greater…

A: The ground-state energy of a proton trapped in a one dimensional infinite potential well is equal to…

Q: A particle of mass m mves in the infinite square well potential v(x)= 0. if -a/2 to a/2 infinitive…

Q: Determine the probability of finding a quantum particle (restricted to a one-dimensional box of…

Q: Find the Probability (in %) that a particle trapped in a box, L units wide can be found between…

Q: For a particle in a box of length L sketch the wavefunction corresponding to the state with the…

A: Energy eigen values for a particle in a box of length L is : En=n2h28mL2 where,n corresponds the no.…

Q: find the partition function of distinguishable and undistinguishable three particles in two energy…

Q: For a system of fermions at room temperature, compute the probability of a single-particle state…

A: Given Data: The temperature is, T = 293 K. The expression for calculating the probability of a…

Q: A particle is trapped in an infinite one-dimensional well of width L. If the particle is in its…

Q: Consider a particle in a box with edges at x = ±a . Estimate its ground state energy using…

A: We have a trial wave function, ψ=|x|λ-aλ. The energy is given by,<E>=<ψ|H|ψ><ψ|ψ>…

Q: Find the expectation value of kinetic energy E for the = 2 sin(zr) vavefunction (r)

A: Given:- The normalized wavefunction ψ(x) = 2sinπx Find:- The expectation value of kinetic energy…

Q: The eigenfunctions satisfy the condition | Vi (x)m(x)dx = &nm , &nm = 1 if n %3D %3D = m , otherwise…

Q: Consider a particle of mass m, located in a potential energy well. one-dimensional (box) with…

A: Given data : Wave function ψn(x) = K sin(nπxL) , 0≤x≤L0 , for any other…

Q: The ground state energy of a particle in a one-dimensional infinite potential well of width 1.5 nm…

A: Ground state energy of infinite potential well is 20eV and width is 1.5nm Ground state energy of…

Q: The wavefunction of is Ψ(x) = Axe(−ax^2)/2 for with energy E = 3aℏ2/2m. Find the bounding potential…

A: Given wave function of is Ψ(x) = Axe (−ax^2)/2

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: 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: Consider a particle moves in 1-Dimension under the Hamiltonian H =. Let the (x) = Ae) the wave…

A: a wavefunction ϕx=Ae-x/a2 for normalisation ∫-∞+∞ ϕ∗x ϕx dx=1 x2a4=z or A2…

Q: Calculate the expectation value of x2 in the state described by ψ = e -bx, where b is a ħ constant.…

Q: An electron having total energy E = 4.50 eV approaches a rectangular energy barrier with U = 5.00 eV…

A: (a) To determine the transmission coefficient, first, it needs to determine the constant α by the…

Q: An anharmonic oscillator has the potential function V = 1/2.(k.x^2) + c.x^4 where c can be…

A: The additional terms cx4 is the perturbation to the idea, harmonic oscillator. Energy correction to…

Q: An electron is trapped in a one-dimensional infinite potential well that is 100 pm wide, the…

A: Given : potential well, L = 100 × 10-12 m ∆x = 5.0 × 10-12 m

Q: Suppose a particle of mass m is moving in a one-dimensional potential of a kind -20<x<2a- = (x)A-…

A: The Energy eigenvalue of a particle inside a potential well of side 'a' is given by: En =n2π2ħ22ma2…

Q: Calculate the energy of the nth excited state to first-order perturbation theory for a spinless…

Q: how that ? (x,t) = A cos (kx - ?t) is not a solution to the time-dependent Schroedinger equation for…

A: Given, Wave function, ψx,t = A cos kx - ωt for a free particle, U(x) = 0 We know time dependent…

Q: that the covariant derivate satisfies prove leibniz's rule

Q: Consider the wavefunction for a particle in a one-dimensional box when the level is n = 6. Calculate…

Q: An electron, trapped in a one-dimensional infinite potential well 366 pm wide, is in its ground…

A: Width of potenial well= 366 x 10-12m mc2=5.11 x 103eV Objective- Energy needed to send electron to…

Q: Prove that assuming n = 0 for a quantum particle in an infinitely deep potential well leads to a…

A: Energy of quantum particle in a infinitely deep potential well Momentum of the particle inside the…

Q: One-dimensional harmonic oscillators in equilibrium with a heat bath (a) Calculate the specific heat…

A: The partition function for the 1D harmonic oscillator in equilibrium with a heat bath at temperature…

Q: (i) Obtain the expression for eigenfunctions of a particle trapped in one 1D Infinite potential well…

A: For a particle trapped in one dimensional infinite potential well of length L.

Q: A particle with mass m is in the state 2 mx a +iat ¥ (x,t) = Ae 2h where A and a are positive real…

Q: The wavefunction of is Ψ(x) = Axe−αx2/2 for with energy E = 3αℏ2/2m. Find the bounding potential…

A: Given:

Q: Suppose that in a certain system a particle free to move along one dimension (with 0 ≤ x ≤ ∞) is…

Q: Find the lowest energy of an electron confined to move in a three dimensional potential box of…

Q: The wavefunction for the particle in a one-dimensional infinite potential well is given by n²n?h? ()…

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

An electron is confined to move in the xy plane in a rectangle whose dimensions are Lx and Ly. That is, the electron is trapped in a two dimensional potential well having lengths of Lx and Ly. In this situation, the allowed energies of the electron depend on the quant numbers Nx and Ny, the allowed energies are given by E = H^2/8Me ( Nx^2/ Lx^2 + Ny^2/Ly^2) i) assuming Lx and Ly =L. Find the energies of the lowest for all energy levels of the electron ii) construct an energy level diagram for the electron and determine the energy difference between the second exited state and the ground state?
Given the potential function V = x2y(z+3), determine the electric potential at (3, 4, -6).
b) Find E at (0,4,0) P, = 2 mC 2 (0 4, 0)
Consider the step potential function shown below. Assume that a flux of electrons has energy E and it is incident on a potential barrier of height vo with E > V0. The electrons are traveling in the x direction and they are originated from x = -. i. Find the transmission coefficient between regions l and I ii. Find the reflection coefficient between regions l and II. i. Assume the electron velocity is 2. x10° cm/s, E = V0 /0.1. Find the probability that there is an electron at the distance a = 2 A'after the barrier. iv. Determine the de Broglie wavelength in A? V(x) Incident particles Region I Region II x = 0
Electron transfer between redox centers in proteins is controlled by quantum tunneling. We can model the region between two redox centers as an energy barrier which the electron must cross. If the distance between the redox centers is 0.752 nm and the energy of the electron is 0.976 eV lower than the height of the barrier, what is the probability that the electron will successfully cross to the next redox center?
A thin solid barrier in the xy-plane has a 12.6µm diameter circular hole. An electron traveling in the z-direction with vx 0.00m/s passes through the hole. Afterward, within what range is vx likely to be?
Four different particles are trapped in one dimensional wells with infinite potential at the walls and zero potential inside. The masses of the particles and their energy level, n , are given by: 1. mass=m, n=1 2. mass=2m, n=2 3. mass =3m, n=3 4. mass=4m, n=2 All these wells have the same length L. Rank the kinetic energy of the particles in order of size, smallest to largest. Group of answer choices E3 <E1<E2<E4 E1 = E4 < E2 < E3 E4 <E3 <E2 = E1 E1 < E2 = E4 < E3 E1 < E2 = E3 <E4
one-dimensional A one-particle, system has the potential energy function V = V₁ for 0 ≤ x ≤ 1 and V = ∞ elsewhere (where Vo 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.
Plot the Fermi-Dirac probability of occupation function fFD(E) for T = 0, 10, 100, 200, 300 and 400K.
A particle with mass m is in a field and has the state (in spherical coordinates) : Where N > 0 and a > 0 are fixed numbers. Determine the average kinetic energy of the particles.
(2nx sin \1.50. 2nz Consider the case of a 3-dimensional particle-in-a-box. Given: 4 = sin(ny) sin 2.00. What is the energy of the system? O 6h?/8m O 4h²/8m O 3h2/8m O none are correct
If one of the two electrons of a H2 molecule is removed, we get a hydrogen molecular ion H+2. In the ground state of an H+2 , the two protons are separated by roughly 1.5 Å, and the electron is roughly 1 Å from each proton. Determine the potential energy of the system. Specify your choice of the zero of potential energy.