Classically, if a particle is not observed, the probability per unit length of finding it in a box is a constant 1/L along the entire length of the box.
(a) Show that the classical expectation value of the position is (1/2)L, that the expectation value of the square of the position is (1/3)L^2 and that the uncertainty in the position is L/(sqrt (12)).
(b) Treat this system quantum mechanically and show that the uncertainty in a particle's position in an infinite well in the general case of an arbitrary n is given by L [1/12 - 1/(2(n^2)(pi^2)]^(1/2).
In what circumstance does this quantity agree with the classical uncertainty?

it was given as a lesson and guide for prayer.

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 .

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in order to follow the instructions and complete the statements, i need to use data from table c of your student guide. can you think of a way to let me see your student guide for a while ? i can't answer the question without the data in table c.