![]() Is used to calculate the energy associated with the particle When the momentum expression for the particle in a box When this is substituted into the DeBroglie relationship it yields momentum ![]() The wavefunction must be zero at the walls and the solution for the wavefunction yields just sine waves.Īnd the higher modes have wavelengths given by The idealized situation of a particle in a boxwith infinitely high walls is an application of the Schrodinger equation which yields some insights into particle confinement. Classical harmonic oscillatorįree particle approach to the Schrodinger equation The Schrodinger equation gives the quantized energies of the system and gives the form of the wavefunction so that other properties may be calculated. The kinetic and potential energies are transformed into the Hamiltonian which acts upon the wavefunction to generate the evolution of the wavefunction in time and space. The detailed outcome is not strictly determined, but given a large number of events, the Schrodinger equation will predict the distribution of results. It is a wave equation in terms of the wavefunction which predicts analytically and precisely the probability of events or outcome. ![]() The Schrodinger equation plays the role of Newton's laws and conservation of energy in classical mechanics - i.e., it predicts the future behavior of a dynamic system. Schrodinger equation Schrodinger Equation ![]()
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