00:01
Hello, in the question we have given the wave function that is psi of x is equal to a, e raised to minus bx for the region x is greater than 0 and a, e raised to bx for x is less than 0.
00:20
Now this is a two -sided exponentially decaying function.
00:24
So if we notice this, so this function, sigh of x is nothing but a e raised to b mod of x this is the function actually so this function we have written in this way and we need to find out the potential energy and the energy eigenvalue now for this kind of wave function though we get the delta function the potential is the delta function so for this kind of wave function we will get the delta function.
00:59
We will get the delta function.
00:59
We will get the delta function.
01:00
Potential as a delta function so we will solve by parts so we will consider first for the region x is greater than zero we know our psi of x is equal to a e raised to minus b x so now we will use the scrodinger equation scrodinger equation is minus h cross square upon 2m d2 si by d x square plus v si si v si is equal to e si so this is the scrawdinger equation now if we plug the value so we have to find out first we have to first find out d2 si by d x square so d si by d x will be equal to minus b a e raised to minus b x and d2 si by d x square so d2.
02:05
Si by dx square will be equal to b square a, e raised to minus bx.
02:14
So if we plug this over here, so we will get this as.
02:18
So it will be minus h cross square upon 2m into b square times a, e raised to minus b x plus v si.
02:30
So v, a, e raised to minus bx, it will be, and that will be...