Development in Time of the Probability Amplitude for a Decaying State

Development in Time of the Probability Amplitude for a Decaying State 

The time-dependent wave function ip(x,y,z t) for the internal motion is expanded as a superposition of solutions of the form (2.15) in the following way 

The coefficients C(m,ni, Em,nitS) are determined from the requirement that at the time t = 0 the wave function ip(x, y, z, t) is equal to a given wave function ip(x,y,z 0). Using (3.1) and (2.49), one therefore finds that 

The probability amplitude p(t) that the electron is still in the initial state ip(x,y,z 0) at the time t( 0) is by definition 

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