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These are questions asked by dcasimir

How can I prove that the product of the slopes of two perpendicular lines is -1?


Is there  a rule similar to cos(n*pi) = -1^(n) for sin(n*pi/2)?

I know for the sin(n*pin/2) it's zero when n is even.

How would a similar rule look for odd integers n, or for all integers n for the case of the sine function?



I'm trying to use the scientific constants package to evaluate the product of certain constants. 

What I'm trying to calculate is the value

(mu*e^(4)/(2*hbar^2), where mu is the reduced mass of the electron and proton, and hbar is Plancks's Constant divided by 2*Pi.

This is for a Quantum Mechanics problem where I'm supposed to show for the large quantum number limit, i.e. large n, this angular frequency approaches values for the classical angular frequency of an ordinary rotating object.

Suppose that the Hamiltonian is invariant under time reversal:

[H,T] = 0.

Show that, nevertheless, an eigenvalue of T is not a conserved quantity.



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