Consider the particle in a one-dimensional box (0 s x s l). assume a term is added to the hamiltonian of the form: πχ v(x)g sin sketch the potential and the expected eigenfunction (small g). in the limit of small g, find the second order correction to the ground state energy 2. (50 points) for a diatomic molecule rotating in free space, the hamiltonian may be written: 12 21 where l is the total angular momentum operator, and i is a constant (the moment of inertia). remember (0 eigenfunctions for the θ π; 0 φ 1 state are: 2π) and d-sin θ d θ d φ.

Asmall blob of putty of mass m falls from the ceiling and lands on the outer rim of a turntable of radius r and moment of inertia i0 that is rotating freely with angular speed ω0 about its vertical fixed-symmetry axis. (use any variable or symbol stated above as necessary.)

Ais useful when you need a simple machine to you separate two things. a. lever b. screw c. pulley d. wedge

The frequency of vibrations of a vibrating violin string is given by f = 1 2l t ρ where l is the length of the string, t is its tension, and ρ is its linear density.† (a) find the rate of change of the frequency with respect to the following. (i) the length (when t and ρ are constant) (ii) the tension (when l and ρ are constant) (iii) the linear density (when l and t are constant) (b) the pitch of a note (how high or low the note sounds) is determined by the frequency f. (the higher the frequency, the higher the pitch.) use the signs of the derivatives in part (a) to determine what happens to the pitch of a note for the following. (i) when the effective length of a string is decreased by placing a finger on the string so a shorter portion of the string vibrates df dl 0 and l is ⇒ f is ⇒ (ii) when the tension is increased by turning a tuning peg df dt 0 and t is ⇒ f is ⇒ (iii) when the linear density is increased by switching to another string df dρ 0 and ρ is ⇒ f is ⇒