The Energy of Spin-Orbit Coupling

Can you show that the energy of interaction is proportional to the scalar product s∙l.? See attachment for symbols. The energy of a magnetic moment mu in a magnetic field B is equal to their scalar product (see attachment). If the magnetic field arises from the orbital angular momentum of the e...

Addition of angular momenta

Please help with the following problems. Suppose you know that an electron is in l = 1 state. As usual we refer the total angular momentum by J = L + S. (a) What does | j = 3/2, j2 = 3/2> state correspond to in terms of the states in the product basis, | l2, s2 >? (b) By acting J_ on this st...

Addition of Angular Momentum in a Helium Atom

Hello, I have attached a homework problem I need help with as a Picture file. With my exam only a day away, I'm unfortunately stuck trying to get to the solutions to these problems before I can fully attempt them myself, so that I can study them for the exam and get as much preparation possible. The...

Quantum Harmonic Oscillator and Normalizing a Wave Function

Hi, I've attached the problem as a Picture. I've learned a lot from the help I have received here on Brainmass, and I'm going to try doing this one on myself and hopefully I'll do it right. Thank you for your help! Consider a simple harmonic oscillator with an angular frequency w. Suppose at t=0 ...

Electron Trapped in Infinite Potential Well

Hi, I've attached a homework problem I need help with as a JPEG picture file. I've done a few slightly easier ones before, and I'm about to try doing this one, but I still make stupid mistakes that I don't catch and would appreciate your help with the problem. Thank you very much! 1. An electron ...

Expectation Values For Various States on a Harmonic Oscillator

See the attached file. 3. (a) Calculate the expectation values < x >, < p >, < x^2 > and < p^2 > for the ground state, | 0 >, and the first excited state, | 1 >, of the harmonic oscillator. (b) Now compute delta(x)delta(p), does this satisfy the uncertainty principle? 4. Using the results f...

States of a Quantum Harmonic Oscillator

6. Consider the state of a harmonic oscillator initially (t=0) to be given by |phi >= 5|0 + 12| 1>. (a) Find the normalized state. (b) What will be the state of the particle after time t. (c) Calculate < x > and < p > for this state at time t. Is this classically what you would expect?

A Two State System Spanned by Two Orthonormal Vectors

Consider a two state system spanned by two orthonormal vectors, |1> and |2>. The action of an operator  is defined via: Â|1> = 2|1> + i|2> Â|2> = -i|1> + 3|2> Find Â|ѱ> where |ѱ> = |1> + |2> Can you now verify your answer for Â|ѱ> by doing the calculation in matrix representati...

Uncertainty: Particle in a Box

A helium atom is confined to a one-dimensional space 8 x 10^-10m. 1. What is the minimum uncertainty in the momentum of the helium atom? 2. What is the minimum velocity of the helium atom? 3. What is the minimum energy of the helium atom?

Phy science/ Bill Tillery 8th edition

1. An electron with amass of 9.11*10 -31 kg has a velocity of 4.3*10 6m/s in the innermost orbit of a hydrongen atom. What is the de Broglie wavelength of the electron? 7. An electron wave making a standing wave in a hydrogen atom has a wavelength of 8.33*10 -11m. If the mass of the electron is...

Quantum Mechanics Multiple Choice

True/False Indicate whether the sentence or statement is true or false. ______ 1. In computer mathematical simulation, a system is replicated with a mathematical model that is analyzed with the computer. ______ 2. Random numbers generated by a mathematical process instead of a physical ...

Dirac Notation for a Quantum State of a System

In the dirac notation for a quantum state of a system, an eigenstate wave function u_n is replaced by the vector |n>, and a general state wave function (see attached) a) Translate the following mathematical statements to the corresponding forms n wave mechanics: i) <n|m> = (see attached), where A...

'Quantum Mechanics'

This question is from the text book 'Quantum Mechanics' second edition by David J. Griffiths. (See attached file for full problem description) --- Problem 3.27 - Sequential measurements. An operator Aprime, representing observable A, has two... ---

The Mathematical Methods in Physical Science

The Pauli spin matrices in quantum mechanics are sigma_x = 0 1 sigma_y = 0 -i sigma_z = 1 0 1 0 i 0 0 -1 a) Show that (sigma_x)^2 = (sigma_y)^2 = (sigma_z)^2 = I (identity of unit matrix) b) Show that (si...

Anti-hermitian operator

This is problem 3.26 in Griffiths' Introduction to Quantum Mechanics (second editition): An anti-hermitian (or skew-hermitian) operator is equal to minus its hemitian conjugate: (a) Show that the expectation value of an anti-hermitian operator is imaginary. (b) Show that the commutator of t...