Which is the Schrodinger equation for a 1D harmonic oscillator:h2 d22 m dx2= Eph2 d22u dx2 + kx2 Jp = Ep2и dx2L2 Y(0,4),,m = h² I(I+1) Y(0,$),md2PO (1-x²)dx2dP2x+ | |(I+1)dxm21-x2P(x) = 0Identify the kinetic energy operator:Identify the potential energy operator:

The harmonic oscillator Hamiltonian is given by, H=p22m+12kx2 Here, m is the mass, k is the force…

Answered: Which is the Schrodinger equation for a…

Science

Physics

Which is the Schrodinger equation for a 1D harmonic oscillator:

University Physics Volume 3

17th Edition

ISBN:9781938168185

Author:William Moebs, Jeff Sanny

Publisher:William Moebs, Jeff Sanny

Chapter7: Quantum Mechanics

Section: Chapter Questions

Problem 60P: If the ground state energy of a simple harmonic oscillator is 1.25 eV, what is the frequency of its...

See similar textbooks

Related questions

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

Q: What is the physical interpretation of the wave function in the Schrodinger Equation?

A: Wave function ψ is a mathematical function that describe certain properties of the wave. However…

Q: Schrodinger’s equation is an example of an eigenvalue equation. Which of the following functions is…

A: The correct option is d)

Q: If p=-iħ d/dx is the linear momentum operator. What is its eigenvalue if it is affected on a…

A: if any operator operates on wave function, than the result should be some constant multiplied by…

Q: Schrodinger's Equation

Q: 1/4 Evaluate (Ar)(Ap) for a particle having wavefunction =| B exp 28 (a) 0 (b) (c) (d) h Answer A

Q: Find and for a hydrogen wavefunction of state (2, 0, 0) (n = 2, l = 0, m = 0)

Q: Schrodinger’s equation is an example of an eigenvalue equation. Which of the following functions is…

A: it should statisfy the eigen value equation.

Q: find the lowest energy of an electron confined in a box of length 0.2nm

A: Given: Particle confined: an electron Length of the confined box: L=0.2 [nm]L=2×1010 [m] The lowest…

Q: What is the significance of the wave function?

A: Wave function It is evident that the particle has the dual nature. This means that a wave is…

Q: Find expectation value of position and for an electron in the ground state of hydrogen across the…

A: ..

Q: Consider an electron inside the potential well of dimension 8.9 nm wide. The ground state energy of…

A: As per the Bartleby guidelines I am answering only the first question.

Q: The Steady-state form of Schrodinger wave equation is _____________

Q: A particle of mass m in a harmonic oscillator potential with angular frequency w is in the state (1)…

A: Given A particle of mass m in a harmonic oscillator potential with angular frequency ω is in the…

Q: A one-dimensional harmonic oscillator wave function is…

Q: A 1-D harmonic oscillator is in the state eu(x) = 1/N14 [3¼o(x) – 2µ1(x) + Þ2(x)] are the ground,…

A: The 1-D harmonic oscillator wave function is given by ψ(x)=[3ψo(x)-2ψ1(x)+ψ2(x)] where ψo(x), ψ1(x)…

Q: Check the uncertainty principle for the wave function Vma -ma,x\/h²? V (x) = %3D

A: We have to check the uncertainty principle for the given function.

Q: The number of ways to arrange 6 classical systems on an energy chip of 5 states is A/16900 B/14734…

Q: Find the average (expectation) value of 1/r in the 1s state of hydrogen. Is the result equal to the…

A: The general formula for the expectation value of 1/r is

Q: Two adjacent energy levels of an electron in a harmonic potential well are known to be 2. and 3.64…

A: Given: Two adjacent levels of an electron Ina harmonic well are known to be 2.60eV and 3.64eV.

Q: The distance (spacing) between the energy levels of a harmonic oscillator is: a. Decreasing with n…

A: The energy of nth level of harmonic oscillator is given by E= hf(n+1/2) where f is the frequency of…

Q: Use the Schrödinger equation to calculate the energy of a 1-dimensional particle-in-a-box system in…

A: Problem 1 Wavefunction of particle in a box is given by, ψx=2LsinnπxL

Q: Q2:A) A linear harmonic oscillator Is in a state which is a superpostion of the ground state and the…

Q: The frequency of ana electron in a ring of radius R (e- is trapped and oscillated at the centre) is…

A: Given equation is, f=bR3/2

Q: The normalized solution to the Schrodinger equation for a particular potential is ψ = 0 for x =0.…

Q: How does the probability density function differ from the wave function?

Q: What is the ground-state energy of (a) an electron and (b) a proton if each is trapped in a…

A: Given: width of potential well L =273 pm =273*10-12 m

Q: The normalised wavefunction for an electron in an infinite 1D potential well of length 89 pm can be…

A: The given normalized wavefunction of the electron is ψ=-0.696ψ2+0.245iψ9+gψ4 This electron is in an…

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

Q: An electron with angular momentum {= 1 exists in the state X = A 2 Where A is the normalization…

A: Given, an electron with angular momentum, l = 1 state, Χ = A1-i20

Q: The general solution of the Schrodinger equation for a particle confined in an infinite square-well…

Q: Particle of mass m moves in a three-dimensional box with edge lengths L1, L2, and L3. (a) Find the…

Q: For a particle in a 1-dimensional infinitely deep box of length L, the normalized wave function or…

A: We have to find the probability of finding the particle.

Q: Show that the ground-state hydrogen atom wavefunction is normalized. (if possible with equations and…

Q: The first four Hermite polynomials of the quantum oscillator are H0 = 1, H1 = 2x, H2 = 4x2 − 2, H3 =…

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

Q: Write Schrodinger’s equation for an object in the potential V(x)= (Ax^3+Bx)

A: One dimensional Schrodinger’s equation for an object of mass m in potential V(x) is given as…

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

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

Concept explainers

Blackbody

Q.5 A blackbody radiates how much energy when the temperature of the body is elevated?

Question

Which is the Schrodinger equation for a 1D harmonic oscillator:
h2 d2
2 m dx2
= Ep
h2 d2
2u dx2 + kx2 Jp = Ep
2и dx2
L2 Y(0,4),,m = h² I(I+1) Y(0,$),m
d2P
O (1-x²)
dx2
dP
2x
+ | |(I+1)
dx
m2
1-x2
P(x) = 0
Identify the kinetic energy operator:
Identify the potential energy operator:

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

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

If the ground state energy of a simple harmonic oscillator is 1.25 eV, what is the frequency of its motion?
The first four Hermite polynomials of the quantum oscillator areH0 = 1, H1 = 2x, H2 = 4x2 − 2, H3 = 8x3 − 12x. Let p(x) = 12x3 − 8x2 − 12x + 7. Using the basis H = {H0, H1, H2, H3}, find the coordinate vector ofp relative to H. That is, find [p]H. This is a textbook question, not a graded question
Write Schrodinger’s equation for an object in the potential V(x)= (Ax^3+Bx)
The normalized solution to the Schrodinger equation for a particular potential is ψ = 0 for x <0, and Ψ(x)=(2/a^{3/2}) x exp(-ax) for x>=0. What is the probability of finding a particle at this potential between x = a - 0.027a and x = a + 0.027a? a) 4,7%b)4,1%c)1,5%d)2,9%e)2,0%
The distance (spacing) between the energy levels of a harmonic oscillator is: a. Decreasing with n b. 2 c. constant d. Increasing with n I will rate accordingly. Don
The wavelength of the emitted photon from the hydrogen molecule H2 is 2.30 μm (micrometers) when the vibrational quantum number decreases by one. What is the effective "spring constant" for the H2 molecule in N/m ?What is the "zero point" energy (in eV) of the molecular vibration?
Calculate the transmission probability for quantum-mechanical tunneling in each of the following cases. (a) An electron with an energy deficit of U - E= 0.010 0 eV is incident on a square barrier of width L = 0.100 nm. (b) An electron with an energy deficit of 1.00 eV is incident on the same barrier. (c) An alpha particle (mass 6.64 × 10-27 kg) with an energy deficit of 1.00 MeV is incident on a square barrier of width 1.00 fm. (d) An 8.00-kg bowling ball withan energy deficit of 1.00 J is incident on a square barrier of width 2.00 cm.
Calculate the period of oscillation of ?(x,t) for a particle of mass 1.67 × 10-27 kg in the first excited state of a box of width 1.68 × 10-15 m. Include a sketch of U(x) and ?(x).
Show that the two lowest energy states of the simple harmonic oscillator, 0(x) and 1(x) from Equation 7.57, satisfy Equation 7.55. n(x)=Nne2x2/2Hn(x),n=0,1,2,3,.... h2md2(x)dx2+12m2x2(x)=E(x).
A collection of atoms has 20% of the sample in a state 7.60 eV above the ground state. If these emit coherent radiation, what is the wavelength of the laser light produced in nanometers? (c = 3.00 × 108 m/s, h = 6.626 × 10-34 J ∙ s, 1 eV = 1.60 × 10-19 J) Give your answer as a whole number.
Calculate the standard uncertainty in z if z=Xsinθ using the angle (45.00 ± 0.74) degrees and the value X = (23.60 ± 0.51) z = ___±___
The wavefunction for an electron in the Hydrogen atom is provided in figure 1, where B is a constant, and a0 is the Bohr radius. By inspection and using the angular part of the wavefunction, identify the value of the quantum numbers l and ml, then operate on this wavefunction with Lˆz, and use your result to verify the value of ml identified.