Magnetic Resonance

Magnetic resonance is a phenomenon in quantum mechanics that affects a magnetic dipole when placed in a uniform static magnetic field.[dubious – discuss] Its energy is split into a finite number of energy levels, depending on the value of quantum number of angular momentum. This is similar to energy quantization for atoms, say  in H atom; in this case the atom, in interaction to an external electric field, transitions between different energy levels by absorbing or emitting photons. Similarly if a magnetic dipole is perturbed with electromagnetic field of proper frequency({displaystyle E/{h},}{displaystyle E/{h},}), it can transit between its energy eigenstates, but as the separation between energy eigenvalues is small, the frequency of the photon will be the microwave or radio frequency range. If the dipole is tickled with a field of another frequency, it is unlikely to transition. This phenomenon is similar to what occurs when a system is acted on by a periodic force of frequency equal to its natural frequency.

States with definite energy evolve in time with phase {displaystyle e^{-iEt/hbar }}{displaystyle e^{-iEt/hbar }} ,( {displaystyle |Psi (t) angle =|Psi (0) angle e^{-iEt/hbar }}{displaystyle |Psi (t) angle =|Psi (0) angle e^{-iEt/hbar }} ) where E is the energy of the state, since the probability of finding the system in state {displaystyle |langle x|Psi (t) angle |^{2}}{displaystyle |langle x|Psi (t) angle |^{2}}= {displaystyle |langle x|Psi (0) angle |^{2}}{displaystyle |langle x|Psi (0) angle |^{2}} is independent of time. Such states are termed stationary states, so if a system is prepared in a stationary state, (i.e. one of the eigenstates of the Hamiltonian operator), then P(t)=1,i.e. it remains in that state indefinitely. This the case only for isolated systems. When a system in a stationary state is perturbed, its state changes, so it is no longer an eigenstate of the system's complete Hamiltonian. This same phenomenon happens in magnetic resonance for a spin {displaystyle { frac {1}{2}}}{ frac {1}{2}} system in a magnetic field.