Delocalization of bond length (20 points total) for the harmonic oscillator, the effect of the displacement operator x operating on a normalized wavefunction n (x) can be written as n1n+1(x) + xvn(x) 2μω. (a) use the above relation to calculate the expectation value of x2 of a state with quantum number n.

Apulley with mass mp and a radius rp is attached to the ceiling, in a gravity field of 9.81 m/s2 and rotates with no friction about its pivot.

The dipole moment of the water molecule (h2o) is 6.17x10^-30 c.m. consider a water molecule located at the origin whose dipole moment p points in the +x-direction. a chlorine ion ( of charge-1.60x10^-19c , is located at x=3.00x10^-9m . assume that is much larger than the separation d between the charges in the dipole, so that the approximate expression for the electric field along the dipole axis can be used. a) find the magnitude of the electric force that the water molecule exerts on the chlorine ion. b) what is the direction of the electric force. -x-direction or +x-direction c) is this force attractive or repulsive?

Suppose astronomers built a 140-meter telescope. how much greater would its light-collecting area be than that of the 10-meter keck telescope? express your answer using two sign