The relativistic energy equation lines up nicely with the Pythagorean theorem. Show that and , where is the angle adjacent to the mc2 side of the triangle.
The relativistic energy equation lines up nicely with the Pythagorean theorem. Show that and , where is...
Relativistic case: Starting from equation invert it to get . Restore factors of G and c. Get the expression for V(r), the "coordinate speed," for a particle falling from rest at . Take the Derivative with respect to r to find the location where the maximum coordinate speed occurs. We were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this image
11/05 For non-relativistic half-spin particles in a Fermi gas moving in 3D, determine the constant C if the fermi energy for number density n = N/V where the density of states is for volume V and wavenumber k. Now determine whether atoms, atoms and atoms are bosons or fermions (I don't think you can just multiply the number of electrons by the half-spin, how else would you do it?). We were unable to transcribe this image2 dn V We were...
Using the Dominated Convergence Theorem show that if f is an integrable function on , there exists a sequence of measurable functions s.t. each is bounded and has support on a set of finite measure, and as goes to . We were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this image
Consider the integral , where R is the region enclosed by the lines and . Suppose we use the change of variables . Fill in the blanks for the bounds and Jacobian. We were unable to transcribe this imageWe were unable to transcribe this imagey = -3.0 + 3 We were unable to transcribe this imageWe were unable to transcribe this image
Show that Brewster's Law (where the incident angle i = p ) and Snell's Law together imply that p +2 = 90 degrees. We were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this image
Electrodynamics. Consider a linear medium where and are both zero in the region of interest. Show that the Maxwell's equations are invariant to the transformation where is a dimensionless constant and is a constant but arbitrary angle. In other words, if and are solutions of Maxwell's equations, show that and too. Consider the special case and thus show that, in this sense, the fields and can be interchanged. This property is often named the duality property of the electromagnetic field....
Pendulum. We discussed in class the equation of motion for the simple pendulum: . Here m is the mass of the bob, is the length of the arm, and is the acceleration of gravity, and is the angle of the arm from away from the vertical. The total energy of the pendulum is a sum of the kinetic and potential terms: a. Draw a picture of the pendulum that shows all of the parameters. b. Show that the equation...
Let be a random sample from , where is an unknown parameter. Show that is a sufficient statistics for , where is the sample variance. We were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this image2 We were unable to transcribe this imageWe were unable to transcribe this image
(a) Using the Pythagorean Theorem, we can state that Show that d)d) and (b) We need the potential energy of the marble. This is due entirely to gravity, so U=mgy + C to be such that U-0 when ф 0. where we can choose C to be anything that makes our lives easier. We want What is C? Show that with this choice, 4b (using the expression for s found in (a).)
Assume t=0 for the following wavefunction, , then , and show with the potential energy function V = that the wavefunction has definite energy We were unable to transcribe this imageWe were unable to transcribe this image?7m We were unable to transcribe this image