The general free-particle wavefunction is of the form Treating the system as a wave packet, or photon-like entity where the Planck hypothesis givesįree particle approach to the Schrodinger equation Now using the De Broglie relationship and the wave relationship: Proceeding separately for the position and time equations and taking the indicated derivatives: Presuming that the wavefunction represents a state of definite energy E, the equation can be separated by the requirement The time dependent Schrodinger equation for one spatial dimension is of the formįor a free particle where U(x) =0 the wavefunction solution can be put in the form of a plane waveįor other problems, the potential U(x) serves to set boundary conditions on the spatial part of the wavefunction and it is helpful to separate the equation into the time-independent Schrodinger equation and the relationship for time evolution of the wavefunctionįor a free particle the time-dependent Schrodinger equation takes the formĪnd given the dependence upon both position and time, we try a wavefunction of the form Schrodinger equation Time Dependent Schrodinger Equation
