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where = is the reduced Planck constant.. The quintessentially quantum mechanical uncertainty principle comes in many forms other than position–momentum. The energy–time relationship is widely used to relate quantum state lifetime to measured energy widths but its formal derivation is fraught with confusing issues about the nature of time.
Usually it does not have analytic solution and different numerical methods, such as split-step Crank–Nicolson [33] and Fourier spectral [34] methods, are used for its solution. There are different Fortran and C programs for its solution for contact interaction [ 35 ] [ 36 ] and long-range dipolar interaction [ 37 ] which can be freely used.