For an 1-d harmonic oscillator whose hamiltonian is h- 2m if two given by hln> = hwo (n+ )ln > ., eigenvalues and eigenstates are 1 > +12> 1 2> v2 eigenstates of operator a an are alod> = az 16> where a lof> = a, l6 (20) , what's the probability to measure energy 1) if the state at t=0 is 0 ei at time t (> 0)? (10) 2) for lo> ,0 = lø4> , what's the probability to measure a at time t?

A26 cm object is 18 cm in front of a plane mirror. a ray of light strikes the object and is reflected off the mirror at a 42-degree angle. what is the angle of reflection? degrees what type of image is formed? what is the size of the image? cm

Four point charges each having charge q are located at the corners of a square having sides of length a. find symbolic expressions for the following. (a) the total electric potential at the center of the square due to the four charges (use any variable or symbol stated above along with the following as necessary: ke.) vtotal= (b) the work required to bring a fifth charge p from infinity to the center of the square (use any variable or symbol stated above along with the following as necessary: w=

On a mild saturday morning while people are working inside, the furnace keeps the temperature inside the building at 23degreesc. at noon the furnace is turned off, and the people go home. the temperature outside is a constant 16degreesc for the rest of the afternoon. if the time constant for the building is 3 hr, when will the temperature inside the building reach 18degreesc? if some windows are left open and the time constant drops to 2 hr, when will the temperature inside reach 18degreesc?