00:01
Hello everyone.
00:02
In this problem, we're asked to use the correspondence between the energy ship relationship of e being equal to p squared over 2m for a non -relativistic particle, which gives us the schrodinger equation of ih bar d by dt, si, of x, and t is equal to minus h -bore squared over 2m times d2 by d x squared of si of x and t.
00:24
So we're asked to use this correspondence, right? so we're asked that if this relationship on the left between the energy and momentum corresponds to the wave equation, the schrodinger wave equation on the right, they were asked to find the corresponding wave equation for the following relationship.
00:45
E squared minus p squared, c squared is equal to m squared c to the 4, which is just the relativistic dispersion relationship, or relation, dispersion relation for a relativistic particle of mass m.
00:58
So what could this correspond to? now, if you think about what the operators do, right? so this kind of prescription here, this correspondence tells us that for each instance of the energy, conceive of an operator that is taking ih bar times the time derivative of the particle or the particle's wave function, right? and for each instance of p, for each instance of the momentum, conceive of an operator that is taking a particle.
01:31
Some sort of spatial derivative of the wave function...