Consider the wave function for the ground state harmonic oscillator:1/4&(x) = (mw)¹⁄ª e−m w x²/(2 h)A. Evaluate the integral: dxsymbolic formatting help Consider the harmonic oscillator wave function:-0.4psir0.0 0.2 0.4 0.6т-4-202xaxisA. What is the quantum number for this state? v = 4B. If w = 47.25 ×1015 s-1 evaluate Ĥ₁ =

All parts are solved below.Explanation:

Answered: Consider the wave function for the…

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

Section: Chapter Questions

Problem 21P

See similar textbooks

Similar questions

If the ground state energy of a simple harmonic oscillator is 1.25 eV, what is the frequency of its motion?
The condition of the rigid boundaries demands that the wave function should vanish for x=0 and for x=L because?
Show that the uncertainty in the momentum of a ground-state harmonic oscillator is (where h is h-bar, m is the mass, and k is the spring constant).
Solve the 3-dimensional harmonic oscillator for which V(r) = 1/2 mω2(x2 + y2 + z2), by the separation of variables in Cartesian coordinates. Assume that the 1-D oscillator has eigenfunctions ψn(x) that have corresponding energy eigenvalues En = (n+1/2)ħω. What is the degeneracy of the 1st excited state of the oscillator?
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>
Whether the energy gap for a system decreases, is constant, or increases as the initial quantum number for the transition increases can be determined by calculating the second derivative of the energy level expression with respect to the quantum number. Calculate the second derivative with respect to the quantum number of the energy level expression for a linear rotor, EJ = hBJ(J+1) and also for the harmonic oscillator, Ev = hυ\upsilonυ(v+1/2).
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.
Suppose a wave function is discontinuous at some point. Can this function represent a quantum state of some physical particle? Why? Why not?
Check Your Understanding Which of the following wave functions is valid wave-function solution for Schr0dinger’s equation?
Check Your Understanding Suppose that a particle with energy E is moving along the x-axis and is in the region O and L. One possible wave function is (x,t)={AeiEt/hsinxL, when 0xL otherwise Determine the normalization constant.
If a quantum HO (harmonic oscillator) is excited to its first excited state through absorption of light that has a wavelength of 4.33x 10-6 m, compute for another wavelength that can proceed with this equal transition when the force constant is doubled.
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

SEE MORE QUESTIONS

Recommended textbooks for you

Modern Physics

Physics

ISBN:

9781111794378

Author:

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

Publisher:

Cengage Learning

Physics for Scientists and Engineers with Modern …

Physics

ISBN:

9781337553292

Author:

Raymond A. Serway, John W. Jewett

Publisher:

Cengage Learning

Principles of Physics: A Calculus-Based Text

Physics

ISBN:

9781133104261

Author:

Raymond A. Serway, John W. Jewett

Publisher:

Cengage Learning

Modern Physics

Physics

ISBN:

9781111794378

Author:

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

Publisher:

Cengage Learning

Physics for Scientists and Engineers with Modern …

Physics

ISBN:

9781337553292

Author:

Raymond A. Serway, John W. Jewett

Publisher:

Cengage Learning

Principles of Physics: A Calculus-Based Text

Physics

ISBN:

9781133104261

Author:

Raymond A. Serway, John W. Jewett

Publisher:

Cengage Learning

University Physics Volume 3

Physics

ISBN:

9781938168185

Author:

William Moebs, Jeff Sanny

Publisher:

OpenStax

Classical Dynamics of Particles and Systems

Physics

ISBN:

9780534408961

Author:

Stephen T. Thornton, Jerry B. Marion

Publisher:

Cengage Learning

SEE MORE TEXTBOOKS