Recent content by musik132

taking u = sin^2a(x) and v'=xcos(x) , I get: -a\pi+(2a+1)(2a)\int\limits_0^{\pi/2} Sin^{2a}(x)x +Sin^{2a-1}(x)cos(x)dx Sadly my math isn't great and can't seem to figure out how this would lead to the factorial form. So I tried to integrate by parts again and try to simplify and it just...

\pi/2-(2a+1)\int\limits_0^{\pi/2} \sin^{2a}(x)cos(x)x Sorry I still don't see how to finish the connection. Edit: Didn't see you said twice IBP ill go back and retry this

Our integral \int\limits_0^{\pi/2} \sin^{2a+1}(x)\,dx Has a Factorial Form: {(2^a a!)}^2 \over (2a+1)! What is the process behind going from that integral to that factorial form? My approach which is not very insightful: I used mathematica to calculate the integral to return...

Hmmm, I wonder what it means exactly by distinguishable quantum states. Is this that divide between quantum systems and classical systems because there are some relatively large systems that behave quantum mechanically. And these relatively large system of radioactive isotopes would show...

Radioactivity is independent of the time the radioactive element was produced. If i remember correctly (which is a big IF, correct me if I'm wrong) this has to do with the collapse of the wavefunction into a definite state by "measurements" and then slipping back into a wave to evolve again...

Thanks Vanhees but I have not learned this notation yet which i believe will be the next chapter in the book. Once I get a little bit further ill revisit this calculation to see how this notation might simplify things. Sorry about not posting the work it is a lot to write without knowing...

Homework Statement Knowing the momentum operator -iħd/dx , the expectation value of momentum and the Fourier transforms how can I prove that <p> = ∫dk [mod square of ψ(k)] h/λ. From this, mod square of ψ(k) is defined to be equal to P(k) right? Homework Equations Momentum operator, p...

The vector field F=<y,x> looks exactly like the the direction field for the system dY/dt = {dx/dt = y} {dy/dt = x} A few questions on this: Are the direction field of a system of ODE's the same as a vector field of calculus? In vector calc we take the line integral of a vector field...

The result found in problem 7.1 says that the velocity of the two stage rocket(v1 in the derivation in the link below) < velocity of a single stage rocket(v2). Am i misinterpreting the results since I thought that the purpose of a multistage rocket was to attain higher terminal velocities. If...

so just to check my thinking: Ft = tension Fg = gravity Fc = centripetal Ftcosθ = Fg and Fc=mrω^2=Ftsinθ If ω increases the angle must go up but if the angle goes up doesn't Ftcosθ become less which would mean an increase in tension in order to counteract gravity? So an increase in ω changes...

Hi suppose i had a ball on string and started to rotate it in a circle around my hand. When i increase the speed of the ball it becomes more and more horizontal. The only forces i can think of at play is centripetal and centrifugal forces and the force exerted by my hand and gravity. Is somehow...