00:01
So in this question, we have a particle in a three -dimensional cubicle box and we have been asked to calculate the planes where probability distribution function this is size square equal to zero.
00:14
So we will start with writing the wave function for a particle in a box of three -dimensional box, which is this and then we to calculate the probability distribution function we it by just taking a square because it's a simple function of trigonometric functions.
00:34
So to make the size square equal to zero, the possibilities are either this function is zero, this function of zero, or this function is zero.
00:45
It means sine is zero.
00:48
So we will calculate si square equal to 0 for these states and compare it with these two states.
00:58
So we will start with calculating the size square for this state.
01:05
We are nx equal to 2 and y equal to 2 and n z equal to 1.
01:13
So for n x equal to n x equal to 2 and n z equal to 2 and n z 2 to 1 equal to 0 0 0 l over 2 q sine squared 2 by x over l sine squared to x over l sine square 2 by y equal to l and si squared by z equal to l to l to make this equal to 0 as said any one of these functions could be zero so i'll start with exploring this so sign 2 pi x or l could be 0 if this argument is integral multiple of pi so i can write as sine 2x equal to 0 if 2x if 2x or l is equal to some integral multiple of pi.
02:48
This n is different than nx and y and z, where n could be 0, 1, 2, and so on.
02:58
So we will start exploring this n.
03:01
If n is 0, it means n equal to 0 means x equal to 0 is a wall.
03:16
For n equal to 1, x is equal to l by 2.
03:26
And n equal to 2, x is equal to l.
03:32
This is also a wall.
03:34
And if i take any value of n greater than 2, it will go out at the box, which is not required.
03:41
So this value of x, which is l by 2, is one plane other than the valve for this component...