The purpose of this question is to motivate the introduction of the â and â' operators for the harmonic oscillator system. we will adapt the simple formula (а — іb)(а + ib) = a2+82 for real numbers a and b. (a) take the harmonic oscillator hamiltonian 1 +mu22 — н 2m 2 and write it in the form hw(q22) q and q is proportional to p, and § is proportional to â. find where in terms of p and â. (b) what is the point of factoring out hw? (c) show that [ë, qi = (d) expand (iq)(e + iq) and simplify. (e) hence show that h can be rewritten as q. and relate â and â* to £ and (f) show that [â, â*] = 1. (g) let {|n)} be the orthonormal energy eigenstates of the harmonic oscillation. recall that the energy eigenvalues are hw (n + 2). use the raising and lowering operator formalism to compute (n| f4 |n).

What is the magnification of a real image if the image is 10.0 cm from a mirror and the object is 50.0 cm from the mirror ? use the equation m=-di/do. a. -5.0 b. 5.0 c. 0.20 d. -0.20

During physical science, ms. greene challenged her students to produce an energy transformation. james and jill wrapped a 4-inch nail with a coil of fifty turns of wire. they connected one end of the coil to one terminal of a knife switch. they connected the other terminal of the knife switch to the battery. finally, they connected the end of the coil to the other terminal of the battery. james held the tip of a 1-inch nail near the flat end of the 4-inch nail. jill closed the knife switch quickly and then opened it. the 1-inch nail was pulled toward the 4-inch nail. what is the best explanation of why the nail moved? a) electrical energy was converted to mechanical energy in the 1-inch nail. b) the 4-inch nail became an electromagnet and the magnetic force attracted the 1-inch nail. c) the electric current in the 4-inch nail was converted to mechanical energy in the 1-inch nail. d) the 4-inch nail had a positive charge and the 1-inch nail had a negative charge. opposites attracted.

The image shows the positions of a car on a roller coaster track. arrange the cars in order based on their gravitational potential energy. begin with the lowest potential energy and end with the highest.