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Ramore precession

2021-05-04 16:42:16 linqy

 It is proved that the precession frequency of lamore is γB Two methods of 

1 Classical method

The moment produced by the magnetic field is

From the moment form of Newton's second law

The change of angular momentum is perpendicular to angular momentum , It's just a change of direction , The size is the same .

The ramore precession frequency is

The image analysis shows that  Precession diagram

The resulting

2 Quantum methods ( Consider only spin precession )

(1) The two-state system is Bloch The representation in the ball

Any two-state system can be expressed as

among ,

This replacement doesn't lose any information .

It can be seen that , The state of the system can be determined by Bloch The unit vector in the ball Express .

From this unit vector in z The projection of an axis easily reverses the probability of which state it is in .

ps: If it is extended to mixed ensemble , The total density operator is the ensemble mean of the pure state density operator .

(2) The evolution of density operators over time

The Hamiltonian of the system is

From the Schrodinger equation

When the Hamiltonian does not contain , The time evolution of the available state is

among , The time evolution operator is

therefore , The density operator is

among , , stay Bloch Around the ball z The matrix of axis rotation is

therefore , From a two-state system , The effect of magnetic field on spin is also based on Ramore frequency Precession in the direction of the magnetic field .

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