Please try to make it clear from the outset what it is you have and what it is you want. You said it involved "three special functions in a summation." There is nothing on p 1484 like that. The formula I quoted is derived much later in the chapter, using Green's functions and steepest descent, but I see no point in pursuing it only to be told you have it already.aim1732 said:Thank you but you know I already have the result.I do not know how to get there however.Yes it is exactly what I am looking for but I think I would require a bit more.
Bill_K said:[Taking my copy of Morse and Feshbach from beneath its helium-filled bell jar...]
Please try to make it clear from the outset what it is you have and what it is you want. You said it involved "three special functions in a summation." There is nothing on p 1484 like that. The formula I quoted is derived much later in the chapter, using Green's functions and steepest descent, but I see no point in pursuing it only to be told you have it already.
The Classical Limit formula for differential cross section for Hard Sphere is a mathematical expression that describes the probability of a particle being scattered by a hard sphere target, based on its impact parameter and the size of the target.
The Classical Limit formula is derived by solving the equations of motion for a particle interacting with a hard sphere potential. This results in an expression for the differential cross section that takes into account the impact parameter and the size of the target.
The main assumptions made in the Classical Limit formula are that the particle and the target are both classical, non-relativistic, and interact through a hard sphere potential. Additionally, the impact parameter is assumed to be much larger than the size of the target.
The Classical Limit formula is a simplified model that does not account for quantum effects or the internal structure of the target. Therefore, it may not accurately predict the exact results of experiments. However, it can provide a good approximation in certain cases, such as when the target is significantly larger than the particle.
The Classical Limit formula is specifically derived for the scattering of a particle by a hard sphere target. However, similar principles can be applied to other types of interactions, such as the scattering of particles by other types of potentials. Modifications may need to be made to the formula to account for different types of interactions.