Recent content by bikashkanungo

From theory, we know that Boltzmann entropy for a given distribution, defined through a set of occupancy numbers {ni}, of the macrostate M, is given by: S=k log(Ω{ni}) where omega is the number of microstates for the previously given set of occupancy number, {ni} . Assuming that the system...

yeah i know that U = exp[-iH*(t-t0)/ħ] if H does not depend explicitly on time .

Can anyone explain how the time evolution operator commutes with the Hamiltonian of a system ( given that the the Hamiltonian does not depend explicitly on t ) ?

<P|¯UU |P> is positive and ¯UU =1

I got the same expression in another quantum mechanics lecture by Dr. Fitzpatrick of Texas A&M . Here is the link http://farside.ph.utexas.edu/teaching/qm/lectures/node27.html

@nileb : No its exactly as given in Dirac's book , I did not leave out any paranthesis

In Dirac's text regarding displacement operator it is given that :- lim(δx→0)⁡[D*exp⁡(iy)-1]/δx =lim(δx→0) [D-1+iy]/δx = dx + iax Where dx = displacement operator =lim(δx→0) [D-1]/δx ax = lim(δx→0) y/ δx and it is assumed that y tends to zero as δx tends to zero can anyone explain how...

In Dirac’s text the equation ¯UUα=α¯UU is well proven . Next it is said that since ¯UU commutes with all linear operators so it must be a number . Further since ¯UU and its complex conjugate are same so ¯UU is a real number . Also Dirac mentions that for any ket |P> , <P|¯UU |P> is positive...

I have a doubt from Dirac’s book which states that , Pr =-iħ∂/∂qr This equation was concluded after stating that the linear operator iħ∂/∂qr satisfy the same commutation relations with the q’s and with each other as p’s do. Next it is stated that(Dirac, p-92) “ This possibility enables us to...