Nick Kidman

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Actress with an interest in the philosophy of science.

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 Oct29 revised Adjoint of a Wave Function \langle\langle\langle Oct29 suggested suggested edit on Adjoint of a Wave Function Oct29 comment Anharmonic oscillator solution function Yeah, and as has been said twice now, you find your differential equation in this form on the Wikipedia page for the Jacobi elliptic function $sn$ - the theory behind this equation isn't so simple and if you need to let the constant of integration unspecified, I could at best copypaste the ugly Mathematica/Wolframalpha solution. Oct29 comment Anharmonic oscillator solution function @bluesquare: Yeah I'm there, but I don't know how to generally solve your equation and in any case I think it's rather complicated. As the user above said, the software programs give solutions in terms of the Jacobi elliptic function - you can look at wikipedia and maybe find a form of your equation there. And you say "No 2 was there in my expression" ... well since the term reads $-\tfrac{1}{2}x^4$ and you must take the derivative $-\tfrac{\mathrm d}{\mathrm dx}(-\tfrac{1}{2}x^4)=\tfrac{1}{2}4x^{4-1}=2x^3$ of it, it's obvious that there indeed is a factor of 2. Oct28 comment Anharmonic oscillator solution function Mhm, seems tricky. The equations of motion should be $x''(t)=-(x(t)-2\ x(t)^3)$ right? Are you sure that $\tanh$ is even a solution of that? Oct28 comment Anharmonic oscillator solution function A differential equation gives a family of solutions. For exmaple you $x(t)=\tanh(t/\sqrt 2)$ implies $x(0)=0$. There will also be a solution for $x(0)=9001$ and, for suitable $x_0$, for $x(0)=x_0$. Find $x(t)$ with unspecified $x_0$, and then plug that $x(t)$ into $H(x(t),x'(t))\overset{!}{=}E$ and solve for $x_0$ as function of $E$. Oct28 comment Anharmonic oscillator solution function Where is your constant of integration from solving the equation of motion? Oct26 comment How to imagine the first few moments of an LR circuit? "Newtons law says $m\frac{\mathrm d}{\mathrm dt}v=F"$. Say there is a ball at rest with $v=0$ and at $t=0$ I kick the ball with force $F=10N$. But how? Since there's no velocity at all." Oct25 comment Free energy variations @usumdelphini: Yes, for each or the $p_i$'s. This is what links to "[note 5]" in the wikipedia article. In fact, it's even more general there, as the functional integrand there is allowed to have higher derivatives in $p$ than only the first one $\nabla {\bf p}$. Oct25 comment What are orbifolds and why are they useful and interesting for physics? I take it this denotes the plane and rotations around $(0,0)$. Oct25 comment What are orbifolds and why are they useful and interesting for physics? The cone with or from which group action? Oct25 comment Understanding the Wave Function and Excited States As far as "live in" should be used at all, I'd not say "the wave function lives in $\mathbb R^3$" is wrong talk. On the other hand, I'd much more have a problem with "does that mean that all other bases must be zero?". I also don't understand your last sentence: "The state can be described using one basis. The wave function must describe all the possible states, which are infinite." Oct24 comment Electrons of conductors Free? @rijulgupta: Firstly, I don't speak of giving temperature to the conductor, I speak of the conductor having measurable temperature at all. Secondly, if the elecrons would vibrate (within the atoms or not), then they would move - vibration is movement too. Oct24 comment Free energy variations @usumdelphini: Eventually $f$ must be scalar. Of course. There is no significant difference between grad and curl within $f$, you should view it as containing all components $\frac{\partial }{\partial x^i}f$. Componentwise functional derivative is straightforward and described in the beginning of the article. It's essentially just like normal differentiation, you do it in all directions and collect the terms. Oct24 comment Electrons of conductors Free? @rijulgupta: I don't quite understand your logic. You want to have the positively charged ions moving (hence also have a varying electrical field, which they produce) and the electrons (which feel these changing electrical fields from the ions) stand still? Oct24 answered Free energy variations Oct24 comment Electrons of conductors Free? @rijulgupta: Well yes: If you assume the opposite, then the notion of temperature of the solid wouldn't make sense. If you can measure the temperature when in contact with the system, and you then leave the system alone, assuming no particles are moving would imply the energy of the solid vanished. Oct24 comment Electrons of conductors Free? @rijulgupta: Which effect do you mean? One can make collision experiments with electrons and the theory of electrons with velocity distributions according to the Boltzmann equation gives accurate results. Oct24 comment Electrons of conductors Free? The way you'd be able to measure a magnetic field is via acceleration of nearby charged particles with velocity $w$. The force they feel is given by $F=w\times B$. By Newton, the forces from all the electrons have to be added up: $\sum_i F_i$ and since $w$ in your experiemtn is fixed, the magnetic field the solid generates would be $\sum_i B_i$, i.e. the effect is linear and no net velocity results in no net magnetic field. In any case, microscopically speaking you can't measure any properties of the solid without applying an electrical field to it: If you shine light, you have an E field. Oct24 comment Electrons of conductors Free? Regarding magnetic field $B$: If you have an isotropic distribution of velocities, the expectation value $\langle {\bf v} \rangle=\int_{\mathbb{R}^3} {\bf v}\cdot f({\bf v})\ \mathrm d^3v=4\pi\int_0^\infty |{\bf v}|\cdot f(|{\bf v}|)\ \mathrm d^3|{\bf v}|=0$ is zero and hence $B$ is too.