00:01
And in this question, you really look at the first, i mean the grand state and the first states of a harmonical state, all right? the way functions for the ground state is psi 0x equals, well, basically constant alpha over pi, 4 over 4, 1 minus x squared over 2.
00:23
And the first exited state is alpha over pi, 1 over 4, squared, of 2x minus x squared over 2, right? so these are two wave function with these two states, respectively.
00:37
And the alpha is a constant that has something to do with the mass of the harmonic oscillator and also, of course, frequency of the hormonal calculator, and as well as probably the plant constant, right? but anyway, i see relevant to us.
00:50
So what is the most probable values of x? the most probable factors, like, was the maximum of this wave functions, right? so the maximum of the wave function, in the ground state obviously is x equal zero, right? so in the ground state, the most problem value is x squared zero.
01:07
But in the excited states, in the first excited state, the most probability is not really x equals zero.
01:13
And you need to differentiate side 1 over x, and you'll find this, you find this proportionate to e minus x squared over 2, and plus e minus x squared over 2 times minus uh, yeah, this a, uh, yeah, uh, x times equal this and minus, uh, and this has to be at zero, you'll find the most probable values x equals, um, x equals one, right? uh, that's, that's what's happening.
01:51
So that's the, uh, most probable value for x in this side state.
01:54
And then you can also calculate the average value of px and xp, right? so for example, when you calculate, calculate the, uh, the, the value of px, actually.
02:03
So calculate value of px, i suppose p is the momentum, and then this is given by dx, of course, times si...