TY - JOUR
T1 - Energy spectrum for a modified Rosen-Morse potential solved by proper quantization rule and its thermodynamic properties
AU - Dong, Shi Hai
AU - Cruz-Irisson, M.
PY - 2012/4
Y1 - 2012/4
N2 - We apply our recently proposed proper quantization rule, ∫ xB xAk(x)dx-∫ xB xAk(x)dx = nπ, where k(x)=√2M[E-V(x)]/h{stroke}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 Φ(x)or the number of the nodes of the wave function ψ(x) increases by one, the momentum integral ∫ xB xAk(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.
AB - We apply our recently proposed proper quantization rule, ∫ xB xAk(x)dx-∫ xB xAk(x)dx = nπ, where k(x)=√2M[E-V(x)]/h{stroke}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 Φ(x)or the number of the nodes of the wave function ψ(x) increases by one, the momentum integral ∫ xB xAk(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.
KW - Energy spectrum
KW - Modified Rosen-Morse potential
KW - Partition function
KW - Proper quantization rules
UR - http://www.scopus.com/inward/record.url?scp=84857950776&partnerID=8YFLogxK
U2 - 10.1007/s10910-011-9931-3
DO - 10.1007/s10910-011-9931-3
M3 - Artículo
SN - 0259-9791
VL - 50
SP - 881
EP - 892
JO - Journal of Mathematical Chemistry
JF - Journal of Mathematical Chemistry
IS - 4
ER -