Recent content by Rococo

Homework Statement Let ##g_k = 2cos(k/2)## and ##z=e^{ip(N+1)}## where N is an integer. There are two simultaneous equations: ##E^2 = (g_k + e^{ip})(g_k + e^{-ip}) = 1 + g_k^2 + 2g_k cos(p) ## [1] ##(1+z^2)E^2 = (g_k + e^{-ip})^2 z^2 + (g_k + e^{ip})^2##[2]...

Consider the following metric for a 2D spacetime: ##g_{tt} = -x ## ##g_{tx} = g_{xt} = 3## ##g_{xx} = 0## i.e. g_{\mu \nu} = \left( \begin{array}{cc} -x & 3\\ 3 & 0 \end{array} \right) Now, since the metric is independent of time (t), there is supposedly a conservation law containing...

Homework Statement Consider a 2D spacetime with: ## ds^2 = g_{tt}dt^2 + g_{tx}(dtdx + dxdt)## where: ##g_{tt} = -x## and ##g_{tx}=3## Draw a spacetime diagram showing the null geodesics, including one which passes through the origin. Then show that for a massive object, when ##x## is positive...

Yes, I forgot to say the question mentions that the equations ## z(\tau) = \frac{cosh(g\tau) - 1}{g} ## and ## t = \frac{sinh(g\tau)}{g} ## are in units where ##c=1##. So reinserting factors of ##c##, would these equations become: ##gt/c = sinh(g\tau /c)## ##z(\tau) = \frac{cosh(g\tau /c) -...

Homework Statement A rocket starts at rest from the Earth, moving in the z direction so that in its own instantaneous rest frame the acceleration is always g = 9.8 m/s^2. To an observer on Earth, its position is given by ## z(\tau) = \frac{cosh(g\tau) - 1}{g} ## ## t = \frac{sinh(g\tau)}{g} ##...

Do you say that ##<ψ_0| \hat{x} | ψ_0 >## and ##<ψ_1| \hat{x} | ψ_1 >## are expectation values of position, which for the simple harmonic oscillator, are zero?

Homework Statement A particle in a harmonic oscillator potential in the following state after a time t: ## | ψ(t) > = \frac{1}{\sqrt{2}} [e^{(-iE_0 t/\hbar)} |ψ_0> + e^{(-iE_1 t/\hbar)} |ψ_1> ] ## I want to write an expression for ## <ψ(t)| \hat{x} | ψ(t) > ##. Homework Equations The...

Thank you, I think I see now, that I should have said the 70N is actually the net force ##F_{net}## acting on the block system, which will be equal to ##F - f_g## where ##F## is the 'applied force' and ##f_g## is the friction between the ground and the block system. Then if the force F was...

Homework Statement [/B] In the figure above, block A has mass ##m_A=25kg## and block B has mass ##m_B=10kg##. Both blocks move with constant acceleration ##a=2m/s^2## to the right, and the coefficient of static friction between the two blocks is ##\mu_s = 0.8##. The static frictional force...

Thanks for the response. I have been trying to gain a deeper understanding of the phenomenon of wavefunction scarring and I'll share what I have found in case others searching for this find it useful (most of this explanation is taken from papers I've linked below): It was first noticed by...

I've looked at the Wikipedia pages for the Ehrenfest theorem and Scars. I still don't really understand how the existence of the classical orbits in the wavefunction comes about. I know that the correspondence principle roughly says that quantum physics reproduces classical physics in large...

For a particle in a stadium billiard, it is observed that so-called 'scars' in the wavefunction appear at particular eigenvectors. These scars correspond to classical orbits, for example in the case shown below, which corresponds to a classical orbit of period 6 The paths which can be...

I see, thanks for the clarifications.

Yes. The exam question previous to this asked me to verify that the products of inertia, with respect to the principal axes, were all zero, which I did. So, this explains why the last three terms in Equation 4.8 are zero, and so I am satisfied as to how to arrive at the final answer. Even so...

The key equation is Equation 4.8 in the last article you linked. The symmetry of this particular problem can be exploited, in that we do not need to consider "direction cosines" because the axis along the body diagonal is in the direction of the unit vector: ##\frac{a}{\sqrt{a^2+b^2+c^2}}\hat{i}...