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- what happens during the precession of spin in a magnetic field
In this lecture Lenny Susskind describes a spin in a magnetic field precesses around the axis of the direction of the magnetic field. This description is also frequently found in NMR theory which is a semi-classical theory.
Lenny says if the magnetic field ##B_o## is applied in the ##z## direction and the spin was originally pointing along the ##x## direction, then the spin will precesses around the ##z## axis. Then Lenny describes around 2:02:00 what sounds contradictory. The spin is not actually in the x axis. The spin is in a superposition of states up and down, which are aligned with the ##z## axis. Only the average of the spin is in the perpendicular direction. The how can there be a measurable component of spin perpendicular to z which is precessing??
The description seems to contradict itself. The spin in the magnetic field is represented with an arrow pointing in an oblique direction, yet what is really there is a superposition of states up and down, along Z.
In NMR spectroscopy someone puts a collection of spins in a magnetic field ##B_z,##. Spins exist in the up (lower energy) and down (higher energy) states with some probability corresponding to the Boltsman distribution. The individual spins are described as precessing around the z axis, and the precessions of individual spins not in phase with each other. Then someone applies a radio frequency pulse to the spins, tipping the bulk magnetization (is this the same thing as spin?) into the x-axis and they start to precess around the z axis in phase with each other. what is really happening when a spin "precesses", and what is the difference between these two precessions in NMR?link:
Lenny says if the magnetic field ##B_o## is applied in the ##z## direction and the spin was originally pointing along the ##x## direction, then the spin will precesses around the ##z## axis. Then Lenny describes around 2:02:00 what sounds contradictory. The spin is not actually in the x axis. The spin is in a superposition of states up and down, which are aligned with the ##z## axis. Only the average of the spin is in the perpendicular direction. The how can there be a measurable component of spin perpendicular to z which is precessing??
The description seems to contradict itself. The spin in the magnetic field is represented with an arrow pointing in an oblique direction, yet what is really there is a superposition of states up and down, along Z.
In NMR spectroscopy someone puts a collection of spins in a magnetic field ##B_z,##. Spins exist in the up (lower energy) and down (higher energy) states with some probability corresponding to the Boltsman distribution. The individual spins are described as precessing around the z axis, and the precessions of individual spins not in phase with each other. Then someone applies a radio frequency pulse to the spins, tipping the bulk magnetization (is this the same thing as spin?) into the x-axis and they start to precess around the z axis in phase with each other. what is really happening when a spin "precesses", and what is the difference between these two precessions in NMR?link: