Recent content by Lazy Rat

thank you for your assistance chaps.

So rearranging I get ## dx = \frac {du\: L}{\pi} ## then the ## du ## part becomes the next step in ## \sin du ## ?

Im sorry fresh_42 I am finding difficult to follow that logic. Are you asking what i would get for the constant?

Homework Statement ## \int {sin} \frac{\pi x} {L} dx ##Homework Equations u substitution The Attempt at a Solution If i make ## u = \frac{\pi x} {L} ## and then derive u I get ## \frac {\pi}{L} ## yet the final solution has ## \frac {L}{\pi} ## The final solution is ## \frac {L}{\pi} - cos...

So would i use the fact that ## E_1 = \frac {3}{2} \hbar ω_0 ## which would give ## e^ \frac {- 3iω_0t}{2} ## And ## E_3 = \frac {7}{2} \hbar ω_0 ## which would give ## e^ \frac {- 7iω_0t}{2} ## Am I on the right track?

the specific question goes as so For this equation ## \Psi (x,0) = \frac {1}{\sqrt{2}}(\psi_1 (x)-\psi_3 (x)) ## The system is undisturbed, obtain an expression for ##\psi (x,t)## that is valid for all t ≥ 0. Express in terms of the functions ##\psi_1 (x)##, ##\psi_3 (x)## and ##ω_0##, the...

Homework Statement If the first two energy eigenfunctions are ## \psi _0(x) = (\frac {1}{\sqrt \pi a})^ \frac{1}{2} e^\frac{-x^2}{2a^2} ##, ## \psi _1(x) = (\frac {1}{2\sqrt \pi a})^ \frac{1}{2}\frac{2x}{a} e^\frac{-x^2}{2a^2} ## Homework EquationsThe Attempt at a Solution Would it then be...

Wonderful, Thank you.

Ah yes of course the dr, by clean up the left side you mean don't have the ## \frac d {dr} ## in the equation? Thanks rude man

Ok thanks for clearing up confusion guys I think I may have got there, I have after multiplying out ## ∫ \frac d {dr}( r \frac {dV}{dr}) = ∫ - \frac ρ ε {r} ## Integrating twice ## v(r) = A ~ ln (r) - \frac {ρ r^2} {4 ε} + B ## Is this correct? Thank you

I see, I've epand the brackets not multiplied out. ## \frac d{dr} (r \frac {dV}{dr})= \frac {\rho f} {\epsilon \epsilon_0} r## Is this correct? Can the derivative terms such as ## \frac d{dr} ## be manipulated algebraically, and why is it ## \frac d{dr} ## and not ## \frac {dV}{dr} ## are these...

Hi Ok so first step is to multiply out. Thus we have for ## \frac 1r \frac d{dr} (r \frac {dV}{dr})= \frac {\rho f} {\epsilon \epsilon_0} ## ## \frac 1r \times r + \frac 1r \times \frac {dV}{dr} + \frac d{dr} \times r +\frac d{dr} \times \frac {dV}{dr} =\frac {\rho f} {\epsilon \epsilon_0} ##...

So I get the same because the right side I treat as a constant. The answer is still the Laplace general solution ##V(r)= A~ ln (r)~ + B## Is this correct? Thank you rude man, may try to tackle in spherical.

##-ρf / εε_0## relates to Poisson equation ##pf## is the free charge density and ##ε_0## is the permitivity of free space. So these can be taken as know constants on this occasion. I am looking to achieve a general solution through integrating twice. With a similar equation for electrostatics...

Homework Statement Hi I was wondering if anyone could give me a hand with this problem I'm trying to solve. I am trying to integrate this equation twice. I'm not really sure what to do with the right hand side of the equation.Homework Equations The Attempt at a Solution [/B] The left side...