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The last few days I've been going back to review the solution of the Schrödinger equation for the Hydrogen Atom. I learned this in school years ago and I review it every 5-10 years just to appreciate it again. However, something very basic is now bothering me, and I was hoping someone could clarify this for me.
Most descriptions of the solution say that the Schrödinger equation can be solved exactly for an isolated H atom. I'm thinking about the fact that we typically solve the equation in spherical coordinates with origin centered at the position of the proton. Now, the ratio of proton mass to electron mass is about 1830, so I can understand the logic here, but I'm trying to come to grips with the argument which allows us to assume the proton is like a stationary object generating the potential which constrains the electron. I've never heard talk about the movement or wave-function associated with the proton. Ok, we can say that the solution is just relative to the proton no matter where is moves, but then isn't this frame of reference a non-intertial frame?
I'm not even sure exactly how to phrase my question, but it seems that some approximation is being made here. Are we saying that the time average of the proton position is centered at the origin? Or, that the non-inertial reference frame is approximately an inertial frame. Or, is there some basic quantum principle that I'm missing here? I expect it is the latter, but need some help to come to grips with it.
I know that this is not a classical problem, but I keep thinking about the orbits of two astronomical gravity bound objects. Both objects orbit the combined center of gravity which is not coincident with the center of the larger object. Note that I'm not doubting the validity of the usual approach, but I'm trying to establish the logical argument one should put forth when the origin of the coordinate system is established.
Most descriptions of the solution say that the Schrödinger equation can be solved exactly for an isolated H atom. I'm thinking about the fact that we typically solve the equation in spherical coordinates with origin centered at the position of the proton. Now, the ratio of proton mass to electron mass is about 1830, so I can understand the logic here, but I'm trying to come to grips with the argument which allows us to assume the proton is like a stationary object generating the potential which constrains the electron. I've never heard talk about the movement or wave-function associated with the proton. Ok, we can say that the solution is just relative to the proton no matter where is moves, but then isn't this frame of reference a non-intertial frame?
I'm not even sure exactly how to phrase my question, but it seems that some approximation is being made here. Are we saying that the time average of the proton position is centered at the origin? Or, that the non-inertial reference frame is approximately an inertial frame. Or, is there some basic quantum principle that I'm missing here? I expect it is the latter, but need some help to come to grips with it.
I know that this is not a classical problem, but I keep thinking about the orbits of two astronomical gravity bound objects. Both objects orbit the combined center of gravity which is not coincident with the center of the larger object. Note that I'm not doubting the validity of the usual approach, but I'm trying to establish the logical argument one should put forth when the origin of the coordinate system is established.