Calculate the expectation values of the position, momentum, their squares, and the respective variances a and a, for the n-th stationary state of a particle in the infinite square well (i. e., v (x) )(ih (x) d and express the final result first in terms of en, and also in terms when calculating (p2) 0 if 0 a, and v(x) 00 otherwise) (2) use 2 of a and other relevant constants as required; express the results for o and op in terms of a and other relevant constants. check that the uncertainty principle is satisfied. which state comes closest to the uncertainty limit? plot the probability density for the 5-th stationary state (i. e., for n 5) as a function of r (or x/a) and mark the point corresponding to x .

i'm just gonna leave this comment here, so i can get a challange done-

explanation:

as we know our atmosphere or air have different levels. every level has other gasses, and every gas has another permeability. when the light comes from lower permeability to higher permeability, it changes its direction. so that means that when the light comes from the moon to the earth, it changes it's direction many more times. it basically means that the shape of the light part of the moon is changed on the earth.

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we have been given a quadratic function and we need to restrict the domain such that it becomes a one to one function.

we know that vertex of this quadratic function occurs at (5,2).

further, we know that range of this function is .

if we restrict the domain of this function to either or , it will become one to one function.

let us know find its inverse.

upon interchanging x and y, we get:

let us now solve this function for y.

hence, the inverse function would be if we restrict the domain of original function to and the inverse function would be if we restrict the domain to .

54 degrees incident angle = reflected angle

angle is from normal turned to line of ray