The concept of time dependent schrodinger equation tdse illustrated in. Deriving time dependent schrodinger equation from wave. The derivation of the schrodinger wave equation is given. Then it uses the nonrelativistic energy momentum relation e p2 2m to obtain the free particle schr. Free particles and the schrodinger equation youtube. Recall that we did not derive the tise, we simple constructed a differential equation that is consistent with the free particle wave function. Pdf how to derive the schrodinger equation researchgate. Derivation of the schrodinger equation and the arxiv. Pdf a strict derivation of the free schrodinger equation shan gao. The schrodinger equation in three dimensions particle in a rigid threedimensional box cartesian coordinates to illustrate the solution of the timeindependent schrodinger equation tise in three dimensions, we start with the simple problem of a particle in a rigid box. Pdf derivation of the schrodinger equation shan gao.
The schrodinger equation also known as schrodingers wave equation is a partial differential equation that describes the dynamics of quantum mechanical systems via the wave function. The sc hr o ding er w av e equati on so far, w e ha ve m ad e a lot of progr ess con cerni ng th e prop erties of, an d inte rpretation of th e w ave fu nction, bu t as yet w e h ave h ad very little to sa y ab out ho w the w ave fu nction ma y b e deriv ed in a general situ ation, th at is to say, w e d o not h ave on han d a ow ave. The timedependent schrodinger wave equation derivation is provided here so that students can learn the concept more effectively. Other equations could have been constructed, but it has been found that the tise is the only one that is consistent with. Schrodinger equation derivation and how to use it youtube. It is not possible to derive the schrodinger equation in any rigorous fashion from classical. The sc hr o ding er w av e equati on macquarie university. The trajectory, the positioning, and the energy of these systems can be retrieved by solving the schrodinger equation. The schrodinger equation the previous the chapters were all about kinematics how classical and relativistic particles, as well as waves, move in free space. The potential energy of a free particle is constant and can be chosen to be zero.
A strict derivation of the free schrodinger equation. Questions related to the derivation of the schrodinger wave equation is one of the most commonly asked questions in board exams and various competitive exams. Before we take the giant leap into wonders of quantum mechanics, we shall start with a brief. Free particle wave function for a free particle the timedependent schrodinger equation takes the form. Presuming that the wavefunction represents a state of definite energy e, the equation can be separated by the requirement. We illustrate a simple derivation of the schrodinger equation, which requires only knowledge of the electromagnetic wave equation and the basics of einsteins special theory of relativity. The equation for rcan be simpli ed in form by substituting ur rrr. Pdf we illustrate a simple derivation of the schrodinger equation, which requires. The solutions to the schrodinger equation with potential everywhere zero, the free particle solutions, are introduced and briefly discussed, including the. In this video we see how the schrodinger equation comes out very simply from the conservation of energy.576 1084 997 165 1314 1533 788 1376 313 1381 1079 153 778 738 1352 884 1433 548 991 367 611 238 1499 1289 171 421 752 1180 839 496 510 52 99 1072 654 14 316 676 304 1354 1339 1107