Talk:Morse potential

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[edit] Spectrum

I am confused with the expression for the eigenvalues. It seems to me that expression for ν₀ is incorrect and corresponds in fact to ω₀ (2π difference). Can anybody check? 195.131.214.163 08:36, 11 September 2007 (UTC)

Yes, indeed. I added the denominator 2\pi in the expression for \nu_0. The anharmonicity constant is however correct. --Zbyszek.szmek (talk) 22:23, 10 December 2007 (UTC)

[edit] Notations

Can somebody please fix this page so that there is only one symbol for the vibrational quantum number? 'v' (not nu) is the most commonly used vibrational quantum number (just like in the picture... except somebody used 'nu' instead of 'v', which can be confusing as well). Thanks

I am not an expert on this subject, but I think that we are missing -De in the potential equation, potential of a molecule is negative right? look at:

http://www.users.csbsju.edu/~frioux/h2-virial/virialh2.htm and http://hyperphysics.phy-astr.gsu.edu/hbase/molecule/hmol.html#c1

I have changed the vibrational quantum number to v (AKA " v ") to match the figure. I have also changed the morse constants to ν's, which looks quite a bit like "v", and may confuse some people. Oh well. That gives them the chance to ask "what's ν (new)?"

As for De, I do not favor changing the Morse potential to include such a constant. This article is about the solution to the quantum mechanical system, which is the same, regardless of the (arbitrary) choice of zero for the potential energy. Besides, a Morse potential is also a valid approximation for molecular dissociation on an excited electronic surface, which can produce excited electronic states of the atoms and lead to very different dissociation energies.Zolot 00:55, 24 February 2007 (UTC)

[edit] Zero of the potential

I wonder if it would be better to shift the energy of the morse oscillator downwards, so that all the bound states are less than zero? --HappyCamper 17:57, 23 April 2007 (UTC)

I think this suggestion is equivalent to that above, of subtracting a constant (D_e) from the equation for the Morse potential. I feel that such a term makes the equation unnecessarily complicated, and if anything obscures physical insight. That is to say, I would expect anyone interested in this article probably already understands that the choice of zero potential energy is arbitrary. Also see my comment about excited electronic states, which (adiabatically) correlate to excited states of the atoms in the Morse approximation. Thus, the only physically relevant quantities are the well depth (D_e) and characteristic inverse length (a). Zolot 17:30, 24 April 2007 (UTC)

Many visitors to this page seem to want to re-zero the potential energy function -- which only obscures the physics, as I have already discussed. In response, I have added a brief statement about the zero of a potential energy being arbitrary. Should we also add the discussion, above, about different values being used as the zero? This gets into quite a few ideas that may not be appropriate for a page that's just supposed to be about the Morse oscillator. Zolot 12:15, 17 May 2007 (UTC)

I disagree. I added the alternative formula not because I wanted to re-zero the potential, but because it is a formulation that is also commonly used, and I think it may be helpful to readers who may not immediately recognize the other formulation. Also, it is worth noting that the formula I added is the one originally used by Morse, so it is notable for historical reasons, although I forgot to mention that detail in the article. (Actually, the original formula in the 1929 paper didn't factorize D, so it was something like Dexp(-2ar) - 2Dexp(-ar)). --Itub 14:30, 17 May 2007 (UTC)

Prior to Feb. 2007, the potential on this page was expressed as V(r) = T_o + D_e ( 1-e^{-a(r-r_e)} )^2, algebraically identical to your Dexp(-2ar) - 2Dexp(-ar)), if T_o = -De. Apparently, each of these formulations is commonly used. Which belong on this page? We could list all of them, in which case this page may become another cluttered wiki entry with redundant information. I prefer to list one concise form, and let the reader handle conversion to other formats. Perhaps it should just be emphasized that other formulations are used and are equivalent.

I don't buy the history arguement. Any discussion of calculus (outside of the history of calculus) uses Leibniz's formulation (for it's lucidity), even if Newton's was first chronologically. I don't know if "the history of the Morse potential" is an interesting enough topic to warrant discussion, but make such a section if you like. Zolot 14:35, 18 May 2007 (UTC)

I'm curious, why not simply tack +V(r0) onto the formula? In that form it is generally true for any particular offset specific to the system of interest. —Preceding unsigned comment added by 130.91.197.117 (talk) 19:55, 15 May 2008 (UTC)