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The Hamiltonian of a system of two (spin- 1/2) electron H= ?1?z1+?2?z2 where ?z is the Pauli Matrix, ? is an energy parameter and our subscripts represent the two electrons 1 and 2. What is the basis where this Hamiltonian is diagonal and what is the matrix of the Hamiltonian in this basis?
Use the absolute derivative DA?/Du=dA?/du??(from ?? to ?)A? dx^?/du to prove that the inner (scalar) product of two vectors is preserved under parallel transport on a path if the connection defined on the manifold is a metric connection.
A railroad car with a mass of 25,000 kg rolls into a second stationary car with a mass of 50,000 kg. How fast was the first car moving before the collision
An asteroid is in a nearly circular orbit of radius 5.219 AU about the Sun. Determine the period of this asteroid
A loudspeaker diaphragm is oscillating in simple harmonic motion with a frequency of 330 Hz, What is the magnitude of the maximum acceleration
Is the force attractive or repulsive?
A circular loop of wire having a radius of 6.0 cm carries a current of 0.14 A. A unit vector parallel to the dipole moment of the loop is given by 0.40i -0.92j, Find the magnetic potential energy of the loop
A 61.0 kg skier encounters a dip in the snow's surface that has a circular cross section with a radius of curvature of 12.0 m .If the skier's speed at point A is 7.50 m/s (before entering dip), what is the normal force exerted by the snow on the skie..
For a simple harmonic oscillator with k= 4.0N/m and A=0.75 m, the time between maximum velocity and maximum acceleration is 2.50s. Find the maximum velocity and maximum acceleration
a 220 kg cylinder falls 2.5m in a joule water heater . as the cylinder falls it stirs the water. how much does the water temp change
A bullet is fired through a board 8.0 cm thick in such a way that the bullet's line of motion is perpendicular to the face of the board. Find the total time the bullet is in contact with the board
Suppose you have a rectangular wooden block with dimensions 8.0 cm x 8.0 cm x 9.0 cm that has a density of 0.85 x 10^3 kg/m^3. What is the volume of the wood in the wooden block
The block of mass M slides back along the horizontal surface with a coefficient of kinetic friction mk and eventually comes to a rest. In terms of v4, how far does the block slide during this final leg of its journey
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