Purchase Solution

Quantum Probability of Eigenvalue Measurement

Not what you're looking for?

Ask Custom Question

A particle of spin-one and magnetic moment  is in a uniform ~B field of strength B. At t = 0, the component of the spin along an axis is at angle  with the ~B field direction is measured to be 1hbar. What is the probability that a measurement at time t(> 0 will yield the eigenvalues mhbar (with m = +1; 0, or -1)?

Please view the attached file for the formatted question!

Attachments
Purchase this Solution
Solution Summary

We calculate the probability of measuring each of three possible eigenvalues (z-component of spin) of a spin-one particle precessing in a magnetic field.

Solution Preview

A particle of spin 1 and magnetic moment is in a uniform magnetic field . At the component of the spin along an axis at an angle with respect to is measured to be What is the probability that a measurement at time will yield the eigenvalues (with m equal to 1, 0, or -1)?

We set up a coordinate system in which points in the z-direction and the magnetic moment is initially in the xz-plane. The particle experiences a torque

where S is the spin angular momentum of the particle. The magnitude of the torque is given by

where is the angular frequency of precession of the magnetic moment of the particle about the z-axis. Thus we have

Now the spin angular momentum of the particle at time is ...

Purchase this Solution
Free BrainMass Quizzes
Introduction to Nanotechnology/Nanomaterials

This quiz is for any area of science. Test yourself to see what knowledge of nanotechnology you have. This content will also make you familiar with basic concepts of nanotechnology.

Intro to the Physics Waves

Some short-answer questions involving the basic vocabulary of string, sound, and water waves.

Basic Physics

This quiz will test your knowledge about basic Physics.

Variables in Science Experiments

How well do you understand variables? Test your knowledge of independent (manipulated), dependent (responding), and controlled variables with this 10 question quiz.

The Moon

Test your knowledge of moon phases and movement.

View More Free Quizzes
Related BrainMass Solutions

  • PIB wavefunctions for butadiene

    If, however,  is not an eigenfunction of A, then any given measurement will produce a result which is an eigenvalue of A.

  • Probabilities in spin measurements

    of quantum mechanics is used to compute probabilities of outcomes of spin measurements.

  • Delta function perturbation switched on and off

    A measurement is made at some later time t_2, where t_2 > t_1. a) What is the probability that the particle will be found to be in the excited state n=3?

  • Quantum Mechanics

    What are the probabilities of getting b1 and b2 c) What is the probability of getting a1 after the measrement discussed in (b)

  • Chemistry: The Heisenberg Uncertainty Principle.

    In quantum mechanics, things are even more complicated. Unobserved, the system (in this case an atom) can simultaneously coexist in several quantum states. When we observe the system it collapses into only one of these quantum states.

  • Spin Angular Monentum

    The principal angular momentum number j which is the eigenvalue of J^2 is a *positive* integer number with sequence difference of 1. Angular momentum is a vector in the calssical sense.

  • Angular States in Quantum Mechanics

    The calculations with fully detailed explanations are in the attached file 82921.pdf I assume that you are familiar with some of the subjects of and related to Quantum Mechanics such as the quantum angular momentum, ladder operators, measurement probabilities

  • # problems in Quantum Mechanics

    probability to measure is The two other eigenvalues are Thus the probability to measure energy value of is the sum of probabilities to find the system in either eigenstate.

  • Density of States Problem

    The solution identifies the quantum state of the lowest energy level in a 3-D quantum well that has a zero probability of finding the electron in the center of the

View More Related Solutions