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\(\Psi(x,t)\) One-dimensional time-dependent Schrodinger equation of a particle of mass \(m\) is \[ i\hbar \frac{d \Psi(x,t)}{dt} = - \frac{\hbar^{2}}{2m} \nabla^{2} \Psi(x,t) + V(x) \Psi(x,t)\] where \(\Psi(x,t)\) is the wave-function representing the particle and \(V(x)\) is assumed to be a real function representing the potential energy of the particle.