Rabi formula derivation


According to the results of previous section we know it will oscillate between the two protons with a frequency equal to the Bohr frequency associated with two stationary state E displaystyle E_rangle and E displaystyle E_-rangle of molecule.
That is a 2 cos 2 / 2 displaystyle leftvert arightvert 2cos 2theta /2.
The interaction Hamiltonian for promotion kiabi magasin this system is H B S B B S z displaystyle mathbf H -boldsymbol mu cdot mathbf B -gamma mathbf S cdot mathbf B -gamma B S_z, S z ( ) displaystyle S_zfrac hbar 2sigma _3frac hbar, where displaystyle.Do check the paper Rabi has lots of pretty pictures and also goes into a lot more depth than I am able to do here.The state of a two-state quantum system can be represented as vectors of a two-dimensional, which means every displaystyle vert psi rangle is represented by good coordinates.Notice that if a system is in an eigenstate of a given, the system remains in that state.Let displaystyle gamma be the for the system.196 ISBhort Introduction to Quantum Information and Quantum Computation by Michel Le Bellac, isbn Quantum Mechanics Volume 1.Tata Institute of Fundamental Research.
Let us call R be the distance between them and 1 displaystyle 1rangle and 2 displaystyle 2rangle the states where the electron is localised around P 1 displaystyle P_1 or P 2 displaystyle P_2.
Consequently, this frequency must appear in the absorption and emission spectrum of Ionized hydrogen molecule.
Thus by solving the stationary Schrödinger equation, the state after time t is given by ( t ) e i H t ( 0 ) ( e i E t 0 0 e i E t ) ( 0 ) displaystyle psi (t)rangle efrac -imathbf.
This decomposition simplifies the analysis of the system especially in the time-independent case where the values of a 0, a 1, a 2 displaystyle a_0,a_1,a_2 and a 3 displaystyle a_3 are constants.Rabi oscillations, showing the probability of a two-level system initially in 1 displaystyle 1rangle to end up in 2 displaystyle 2rangle at different detunings.The probability amplitude of finding the system at time t in the state 2 displaystyle 2rangle is given by 2 ( t ) e sin ( / 2 ) cos ( / 2 ) ( e E t e E t ) displaystyle langle.This shows that there is a finite probability of finding the system in state 2 displaystyle 2rangle when the system is originally in the state 1 displaystyle 1rangle.Then, at time t displaystyle t, the probability of it being found in state 2 displaystyle 2rangle is given by P 1 2 ( t ) ( 1 ) 2 sin 2 ( t 2 ) displaystyle P_1to 2(t)left(frac omega _1Omega right)2sin 2left(frac Omega t2right).

If we imagine there is some state that is neither affected by the external magnetic field nor the nuclear fields then we have the The energy shif of the levels with respect to this state is given by E_M-fracDelta E 2(lfrac12).


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