I'm refreshing my quantum mechanics by working through Liboff's text. I'd like someone to double check my work. Here's the homework for chapter one and my answers. I think they're all correct but wish a second opinion, just to make sure. This stuff can get tricky.

1.1 For each of the following systems, specify the number of degrees of freedom and a set of good coordinates.

(a) A bead constrained to move on a closed circular loop.

(b) A bean constrained to move on helix of constant pitch and constant radius.

(c) A particle on a right circular cylinder.

(d) A pair of scissors on a plane.

(e) A rigid rod in space.

(f) A rigid cross in space.

(g) A linear spring in space.

(h) Any rigid body with one point fixed.

(i) A Hydrogen atom

(j) A lithium atom

(k) A compound pendulum (two pendulums attached end to end)

Answer:

(a) Distance along loop from arbitrary fixed point on loop. 1 degree of freedom.

(b) Distance along helix from an arbitrary fixed point on helix. 1 degree of freedom.

(c) Cylindrical coordinates. 2 degrees of freedom.

(d) 3 numbers to locate center of scissors. One for angle scissors make with chosen axis. One for angle scissors is open. 5 degrees of freedom.

(e) 3 numbers to locate center of rod in space. Two numbers to orient rod in space, typically q and f.5 degrees of freedom.

(f) 3 numbers to locate center of rod in space. Two numbers to orient the rod in space. Two numbers to rotate about both axes in space. 6 degrees of freedom.

(g) Three numbers to locate center of spring in space, two numbers to orient spring in space and one number for amount spring is stretched. 5 degrees of freedom.

(h) 3 numbers to locate body in space. 2 numbers to orient body and 2 numbers about each axis of rotation. 7 degrees of freedom

(i) 3 numbers to locate proton in space. 3 numbers to locate the electron in space. 6 degrees of freedom.

(j) 3 numbers to locate the nucleus in space. 3 numbers for each electrons in space. 12 degrees of freedom.

(k) 2 degrees of freedom for first pendulum. 2 degrees of freedom for second pendulum.