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.

Asmall metal bar, whose initial temperature was 10° c, is dropped into a large container of boiling water. how long will it take the bar to reach 70° c if it is known that its temperature increases 2° during the first second? (the boiling temperature for water is 100° c. round your answer to one decimal place.) sec how long will it take the bar to reach 98° c? (round your answer to one decimal place.)

Consider an insulating crystal, made up of layers of atoms. what form would you expect the temperature dependence of the phonon heat capacity to approach at extremely low temperatures if the interlayer coupling is i)very strong (rigid coupling), and ii) very weak. explain.

An architect plans to use solar energy to heat the next house he designs. what principle of absorption and infrared energy can be applied to the design of the new house? how could she apply to those principals?