For a harmonic oscillator in one dimension the lowering and raising operators are detined by 父+1 2ћ 2ћ (a) show that (b) compute the expectation values (c) what can you say about the uncertainty relation axap?

Describe how the motion of a spring being pushed forward and backward is similar to the motion of air particles in a sound wave.

People with normal vision cannot focus their eyes underwater if they aren't wearing a face mask or goggles and there is water in contact with their eyes. in a simplified model of the human eye, the aqueous and vitreous humors and the lens all have a refractive index of 1.40, and all the refraction occurs at the cornea, whose vertex is 2.60 cm from the retina.with the simplified model of the eye, what corrective lens (specified by focal length as measured in air) would be needed to enable a person underwater to focus an infinitely distant object? (be careful-the focal length of a lens underwater is not the same as in air! assume that the corrective lens has a refractive index of 1.62 and that the lens is used in eyeglasses, not goggles, so there is water on both sides of the lens. assume that the eyeglasses are 2.05cm in front of the eye.)

The stopwatch used by a student to measure velocity of a pulse in a slinky was of least count 0.1 second. he stops the stopwatch when a pulse has made 3 journeys from one end to the other of the slinky. he finds the seconds hand to be at 52nd division. calculate the correct time noted by him.