NDLI: Energy spectrum for a modified Rosen-Morse potential solved by proper quantization rule and its thermodynamic properties

Content Provider	Springer Nature Link
Author	Dong, Shi Hai Cruz Irisson, M.
Copyright Year	2011
Abstract	We apply our recently proposed proper quantization rule, $${\int_{x_A}^{x_B}k(x) dx -\int_{x_{0A}}^{x_{0B}}k_0(x) dx=n\pi}$$ , where $${k(x)=\sqrt{2 M [E-V(x) ]}/\hbar}$$ to obtain the energy spectrum of the modified Rosen-Morse potential. The beauty and symmetry of this proper rule come from its meaning—whenever the number of the nodes of $${\phi(x)}$$ or the number of the nodes of the wave function ψ(x) increases by one, the momentum integral $${\int_{x_A}^{x_B} k(x)dx}$$ will increase by π. Based on this new approach, we present a vibrational high temperature partition function in order to study thermodynamic functions such as the vibrational mean energy U, specific heat C, free energy F and entropy S. It is surprising to note that the specific heat C (k = 1) first increases with β and arrives to the maximum value and then decreases with it. However, it is shown that the entropy S (k = 1) first increases with the deepness of potential well λ and then decreases with it.
Starting Page	881
Ending Page	892
Page Count	12
File Format	PDF
ISSN	02599791
Journal	Journal of Mathematical Chemistry
Volume Number	50
Issue Number	4
e-ISSN	15728897
Language	English
Publisher	Springer Netherlands
Publisher Date	2011-10-21
Publisher Place	Dordrecht
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Proper quantization rules Energy spectrum Modified Rosen-Morse potential Partition function Math. Applications in Chemistry Theoretical and Computational Chemistry Physical Chemistry
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Chemistry

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