Several methods are available for computing excited electronic states, including configuration interaction singles ( CIS ), the random phase approximation ( RPA ), and equation-of-motion coupled cluster ( EOM-CCSD ).
12.
Contrast with spontaneous emission ( which dominates in sub-threshold semiconductor lasers and is the primary process by which LEDs operate ), which releases photons of random phase and propagation direction ( and less predictable frequency ).
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In these way excited states can be reproduced by the means of Random Phase Approximation ( RPA ), and eventually consistently calculating also corrections to the ground state ( e . g . by the means of Nuclear Field Theory ).
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In general, starting with a zero phase estimate or a random phase estimate for the magnitude-based signal recovery approach may not result in convergence, where as in the case of the phase-based signal recovery approach, even starting with a constant unit magnitude for the Fourier transform of the estimated signal, results in convergence.
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Where x ( t ) is the time error; x _ 0 is the time error at t = 0; y _ 0 is the fractional frequency error at t = 0; D is the linear fractional frequency drift rate; \ phi ( t ) is the random phase deviation component and \ nu _ { nom } is the nominal frequency.
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