Vibration-rotation coupling in a Morse oscillator

The Morse function is invaluable for describing the vibrational motion of diatomic molecules. The time independent Schrodinger equation can be solved in closed form for this potential only if molecular rotation is ignored or if the rotation is isolated from the vibrational motion by approximating it as a rigid rotor. To find the dependence of the energy eigenvalues on the vibrational and rotational state to a level of approximation that includes vibrational-rotational coupling, a higher level of approximation than the rigid rotor model is required. We present a method that can be understood by undergraduates, thus making the Morse potential a more useful example. The method yields results that are identical to those presented by Morse, but in a more elementary way. (C) 2007 American Association of Physics Teachers.