An electron is at rest in an oscillating magnetic field along the z-direction with B₂-Bo cos(wt) whereBo and are constants.a. Write the Hamiltonian matrix for this spin system.b. The electron starts out at t=0 in the spin-up state with respect to the x-axis, that is x(0)=x+(×).Determine x(t) at any subsequent time. Hint: Solve the time-dependent Schrodinger equationdirectly.c. Find the probability of getting -hbar/2 (hbar-h/2T) if you measure Sy.d. What is the minimum field (Bo) required to force a complete flip in Sx.

Given, An electron is at rest in an oscilllating magnetic fieldis, B→= Bocos w+k^Where Bo…

Answered: An electron is at rest in an…

An electron is at rest in an oscillating magnetic field along the z-direction with B₂-Bo cos(wt) where Bo and w are constants.

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

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Concept explainers

Crystalline Imperfections

The crystalline imperfections are described as the geometrical defects in the crystal due to incorrect arrangement of atoms, impurity, vacancy, and many more. It is not possible to achieve a perfect or ideal crystal, practically.

Question

An electron is at rest in an oscillating magnetic field along the z-direction with B₂-Bo cos(wt) where
Bo and are constants.
a. Write the Hamiltonian matrix for this spin system.
b. The electron starts out at t=0 in the spin-up state with respect to the x-axis, that is x(0)=x+(×).
Determine x(t) at any subsequent time. Hint: Solve the time-dependent Schrodinger equation
directly.
c. Find the probability of getting -hbar/2 (hbar-h/2T) if you measure Sy.
d. What is the minimum field (Bo) required to force a complete flip in Sx.

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