00:01
Now here we look at a few questions regarding the short -linear wave equation, right, which is given by partial h bar, partial over partial t, si -x -t equals minus h squared over 2n, partial squared over partial x squared, si -x -t plus v, si -s -t, right? so this is the short -linear equation.
00:25
And the first question is, i mean, what kind of, i mean, you're asking to interpret this equation in terms of, in terms of differential equation.
00:35
Of course, this is a homogeneous linear second order partial differential equation, right? what physical system is modern, well, it's a, it's a simple particle, right, of mass m moving a potential v, right? so that is, that is the system it describes, it's just a particle, right? what can be determined from the equation if you solve, well, you can determine, of course, if you solve this equation, you can determine the, um, the way function of the, of the particle.
01:04
And from the way of function that you can calculate everything else, for example, the, the, the speed of the particle, the energy of the particle and every, every, every, every physical quantity, okay? every physical observer can be, can be calculated from this way function, right? so you can also, of course, replace the, rewrite this equation in terms of laplace operator.
01:30
Well, because, you know, the, this part, i mean, this, this energy operator, this kinetic energy operates can actually be re -retingized partial h bar the laplace operator squared divided by 2m...