Answered: An electron is trapped in a…

An electron is trapped in a one-dimensional infinite potential well. Show that the energy difference E between its quantum levels n and n + 2 is (h2/2mL2)(n + 1).

Modern Physics

3rd Edition

ISBN:9781111794378

Author:Raymond A. Serway, Clement J. Moses, Curt A. Moyer

Publisher:Raymond A. Serway, Clement J. Moses, Curt A. Moyer

Chapter6: Quantum Mechanics In One Dimension

Section6.4: The Particle In A Box

Problem 2E

See similar textbooks

Related questions

Q: What is the degeneracy of the 4th excited state of a 3-dimensional isotropic harmonic oscillator?

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

Q: The wave function for an electron in an infinite potential well is given as follows; TX sin L 4,(x)…

Q: An electron is trapped in a one-dimensional infinite potential well that is 140 pm wide; the…

Q: The wave function for a quantum particle confined to moving in a one-dimensional box located between…

A: The wave function for a quantum particle confined to moving in a one-dimensional box located between…

Q: Find the probability that a particle trapped in a box L wide and infinite potential we’ll be found…

A: Given: Length of box 'L' wide Potential is infinite The particle will be found between 0.4L to 0.5L…

Q: For a particle in cubic box, what is the degeneracy of the energy level 81 times the ground state…

A: The general expression of the particle’s energy (Enx,ny,nz) in a cubic box of side a is given as,…

Q: A proton is confined to a one dimensional infinite potential well 100 pm wide. What is its…

A: Ground state energy one dimensional infinite potential well E1=h28mpL2=6.626×10-34 J·s281.672×10-27…

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: equation for the particle in a one-dimensional box, the quantization of energy levels results when…

A: Schrodinger wave equation for the particle in a one dimensional box is : δ2ψδx+8π2mh2E-vψ=0

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

Q: An electron is trapped in a one-dimensional infinite potential well that is 170 pm wide; the…

Q: A proton is confined to a one-dimensional infinite potential well 100 pm wide.What is its…

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

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: omment on the value energy separation of free electron in a 1 D infinite potential well when the…

A: Given:- the value energy separation of a free electron in a 1 D infinite potential well when the…

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: A certain atom has a doubly degenerate ground level, a triple degenerate electronically excited…

Q: Consider a particle with 1-D wave-function (x) = kexp(-x²). Sketch (x),

Q: A proton is confined to a one-dimensional infinite potential well 293 pm wide. What is its…

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

Q: An electron is in the ground state in a two-dimensional, square, infinite potential well with edge…

A: The wave function for an electron in a two-dimensional well,

Q: The wavefunction of the particle in its ground state is w(x)= Ae 2a, Calculate the first %3D order…

A: The first-order energy correction is given by: ∫ψ*(x)H'ψ(x)dx∫ψ*ψdx where ψ(x) is the wavefunction…

Q: An electron is trapped in a one-dimensional infinite potential well that is 430 pm wide; the…

Q: An electron is trapped in a one-dimensional infinite potential well that is 470 pm wide; the…

Q: A particle is confined to the 1D infinite potential well of the figure below If the particle is in…

Q: The ground state energy of an electron in a one-dimensional trap with zero potential energy in the…

A: Given : Initial potential energy at the wall, E1 = 2.0 eV Let the initial width of potential well be…

Q: What must be the width of a one-dimensional infinite potential well if an electron trapped in it in…

A: Given: mass of electron, m = 9.1 x 10-31 kg state, n = 3 Energy of electron, E = 4.7 eV = 4.7 x…

Q: The number of methods for arranging two semi-classical systems on a power slice of 4 states is: O 4…

Q: An electron is trapped in a one-dimensional infinite potential well. For what (a) higher quantum…

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 ratio of the energy of the first excited state to that of the ground state of a…

A: In quantum mechanics, a particle in a 3-D infinite rectangular box describes that particle is free…

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

Q: What is the independent wave function for a particle in a box x=0,L

Q: A particle, which is initially (t = 0) in the ground state of an infinite, one-dimensional potential…

A: The ground state and first excited state of the given infinite one-dimensional potential box can be…

Q: Calculate the average or expectation value of the position of a particle in a one-dimensional box…

Q: Find the excitation energy from the ground level to the third excited level for an electron confined…

Q: A one -dimensional potential box of width a. ) Show that the wavefunctrion af a particle in the 2nd…

A: A one-dimensional potential box of width a is illustrated below: The wavefunction for the nth state…

Question

An electron is trapped in a one-dimensional infinite potential
well. Show that the energy difference
E between its quantum levels
n and n + 2 is (h2/2mL2)(n + 1).

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

VIEW

Step 2

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 2 steps with 2 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

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

Can a quantum particle 'escape' from an infinite potential well like that in a box? Why? Why not?
What must be the width of a one-dimensional infinite potential well if an electron trapped in it in the n = 3 state is to have an energy of 4.7 eV?
The ground-state energy of an electron trapped in a onedimensional infinite potential well is 2.6 eV.What will this quantity be if the width of the potential well is doubled?
What is the ground-state energy of (a) an electron and (b) a proton if each is trapped in a one-dimensional infinite potential well that is 200 pm wide?
An electron, trapped in a one-dimensional infinite potential well 250 pm wide, is in its ground state. How much energy must it absorb if it is to jump up to the state with n= 4?
An electron is trapped in a one-dimensional infinite potential well in a state with quantum number n = 17. How many points of (a) zero probability and (b) maximum probability does its matter wave have?
If in a box with infinite walls of size 1 nm there is an electron in the energy state n=2, find its probability density, the wave function and the corresponding energy.
An electron is trapped in a one-dimensional infinite potential well that is 100 pm wide; the electron is in its ground state. What is the probability that you can detect the electron in an interval of width x = 5.0 pm centered at x = (a) 25 pm, (b) 50 pm, and (c) 90 pm? (Hint: The interval x is so narrow that you can take the probability density to be constant within it.)
An electron is trapped in a finite potential well that is deep enough to allow the electron to exist in a state with n= 4. How many points of (a) zero probability and (b) maximum probability does its matter wave have within the well?
An electron is trapped in a one-dimensional infinite potential well that is 460 pm wide; the electron is in its ground state. What is the probability that you can detect the electron in an interval of width δx = 5.0 pm centered at x = 300 pm? (Hint: The interval δx is so narrow that you can take the probability density to be constant within it.)
A particle of mass m mves in the infinite square well potential v(x)= 0. if -a/2 to a/2 infinitive find <p> and <p^2> using wave function shai 1 and compute <p> and <p^2>
Prove that assuming n = 0 for a quantum particle in an infinitely deep potential well leads to a violation of the uncertainty principle Δpx Δx ≥ h/2.