00:01
So in this question we have been asked to calculate the probability distribution function where it is maximum.
00:12
So we have a particle in a box of three -dimensional, which is a cube.
00:19
So to work out, then we will start with a wave function which is a function of space only, which is written as this and as a co -ed -oagued.
00:29
We know this.
00:32
To calculate the public redistribution function, we need to calculate this size square, which is multiple of si into si star.
00:43
So which is this given as an equation 2.
00:47
The question is asking us to calculate the positions or locations where si square is maximum.
00:54
So the question it is given, like if we have particle in a state of nx and y nz equal to one find the maximum size square with maximum for given x y z and same for the part b so we will work out one by one so for part a we will start putting the values of nx and y and z in the given size square gradient which will be this l by 2 sine square and nx is 1 and y is 1 and z is also 1 so to find the location where si square is max basically we are trying to find where sign functions are max and we know that sign maximum values of sine function is plus minus 1 it's like this i'm doing this for the one component only.
02:23
So this is the maximum value.
02:25
It could be plus one or negative one depending on this argument.
02:29
So what are the possible values of the argument which can give us plus one or negative one? so to calculate this, the one positive value, possible value is it could be pi by 2 for sine function to be 1.
02:54
Or it could be possible value of argument could be 3 pi by 2 or sign by x over l equal to minus 1.
03:17
So from this part we can clearly see this will give us x equal to what it's by l by 2 and this will give us possible value of x equal to 3 l by 2 so you can clearly see this is the value of x which we can find within the box so it is allowed value of x and if you see this position which is 3 l by 2 it's outside the box which is not allowed so we can do the same thing for component a, y, and z because ny and n z and x are all the same...