00:01
In this question, you look at the harmonical oscillator.
00:04
At the harmonical oscillator initially it's in the foreign state, psi t equals zero given by, square of two, zero.
00:16
That's ground state and first excited state of a harmonic oscillator.
00:20
And you ask you to calculate the average value of the precision of this harmonic oscillator, right? side t.
00:31
And, you know, we can easily first write out this fraction first.
00:38
In the first place, i want to write down the way function time t, which is simply given by a split of two.
00:47
And the agon state of note, i mean, the ground state evolves by a fifth factor, which is just minus i times an inch with the energy of that is half h omega right half h by omega so divided by h i just say so it would be omega t times two right and zero and plus and for this first for this state you would find actually minus i three omega over two t and one right so that's the state now if you do it you'll find there are actually four possibilities um you will have four possibilities.
01:24
So first, let me just pull this factor up here.
01:27
So you have one over two, right? you have one, you have a square, you have this factor from this part and also from this place, put them together, you get half.
01:35
And then you have four terms.
01:37
The first time, you would come from, of course, you would have come from the grand state, right? so you would have just the ground state x zero, right? like this.
01:50
And the second term, you would come from the first state state, and again, you would find it's 1, x1.
01:57
And then you have the cross terms...