00:01
Hello everyone, for the solution of this question, let's consider the squatteringal equation for first region is minus h squared divided by 2m multiplied by d square x x1 divided by d xx squared plus v si1 equals to e si i therefore minus h squared divided by 2m d square si 1 divided by d x squared x squared is equal to e minus v si 1 now d square si 1 divided by d x squared x squared is equal to minus 2m x square e minus b si 1 therefore, d square, si1 divided by dx squared, my plus 2m, h squared, multiplied by e minus v, x, x, 1 is equal to 0.
01:06
In region first, v is equal to 0 and e is equal to 9v0.
01:13
Therefore, the equation will be d square, si1, divided by d, d, x squared plus 9 2m v0 divided by h square si 1 is equal to 0 now sine k square sine k squared is equal to 2m v0 divided by s square consider k to this therefore the equation will be si square d square x divided by d x squared plus 3k the whole square si1 equals to 0 therefore the solution is given by given as si1 x equals to a sign 3k x plus b cost 3k x this is our equation number first similarly, the crotringer equation is for second region.
02:29
For second reason, the equation will be minus s squared divided by 2m, d square 2 divided by d x squared plus v2, si 2 equals to e.
02:48
So, therefore, the equation will be d square, si2 divided by the x square, plus 2m, s square 9 minus 5, v0, x2 will be close to 0, hence the equation will be d square, si 2 divided by d x square plus 4 k square si 2 is equal to 0 here k is equal k square is equal k square is 2 nv divided by h squared thus the solution of equation is si 2 x equals to c sine 2 k x plus d cost 2 k x this is our equation number 2 similarly, the scrotrangle equations for third region, third region is minus h -square upon 2m, d -square -si -3 divided by tx -square plus v3, s -3, s -3 equals to e -s -3.
04:16
Here v -3 is equal to 10 v0 and e equal to 9 v0.
04:21
On putting the values, we have d square, si3 divided by dx square plus 2 n h square in the bracket 9 v0 minus 10 b0, si3 is equal to 0.
04:43
Therefore the equation will be d square, si3 divided by d x square minus k squared si 3 equals to 0, here k squared is equal to 2m v0 divided by x squared.
05:03
Now the solution of the equation is si 3 is equal to e, e.
05:09
Rest to power kx plus f, e...