• Bulletin of the Korean Chemical Society
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• v.34 no.11
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• pp.3425-3428
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• 2013

We solve the Klein-Gordon equation with the Morse empirical potential energy model. The bound state energy equation has been obtained in terms of the supersymmetric shape invariance approach. The relativistic vibrational transition frequencies for the $X^1{\sum}^+$ state of ScI molecule have been computed by using the Morse potential model. The calculated relativistic vibrational transition frequencies are in good agreement with the experimental RKR values.

• Bulletin of the Korean Chemical Society
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• v.26 no.11
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• pp.1717-1722
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• 2005

The analytical transfer matrix method suggests a new quantization condition for calculating bound state eigenenergies exactly. In the quantization condition, the phase shifts of bound state wave functions scattered at classical turning points are explicitly introduced. We calculate the phase shifts of eigenfunctions of the Morse potential with various boundary conditions in order to understand the physical meaning of phase shifts. The Morse potential is known to adequately describe the interaction energy between two atoms and, therefore, it is frequently used to determine the vibrational energy levels of diatomic molecules. The variation of Morse potential eigenenergies influenced upon by changing boundary conditions is also investigated.

• Bulletin of the Korean Chemical Society
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• v.29 no.1
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• pp.85-88
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• 2008

A direct application of the WKB quantization to the three-dimensional Coulomb potential does not yield the exact eigenenergies. The three-dimensional Coulomb potential is converted to a Morse potential by using the point canonical transformation. Then the WKB quantization is applied to the Morse potential to find a relationship between the eigenenergies of the Coulomb and those of the Morse potentials. From the relationship the exact eigenenergis of the Coulomb potential are determined. The same method is found to be also valid for the three-dimensional harmonic oscillator potential. And the Langer modified WKB quantization is algebraically derived.

• Bulletin of the Korean Chemical Society
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• v.35 no.12
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• pp.3443-3446
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• 2014

We present the solution of Klein Gordon equation with new generalized Morse-like potential using SUSYQM formalism. We obtained approximately the energy eigenvalues and the corresponding wave function in a closed form for any arbitrary l state. We computed the numerical results for some selected diatomic molecules.

• Bulletin of the Korean Chemical Society
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• v.31 no.12
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• pp.3573-3578
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• 2010

Recently it is suggested that it may be possible to obtain the approximate or exact bound state solutions of nonrelativistic Schr$\ddot{o}$dinger equation from relativistic Klein-Gordon equation, which seems to be counter-intuitive. But the suggestion is further elaborated to propose a more detailed method for obtaining nonrelativistic solutions from relativistic solutions. We demonstrate the feasibility of the proposed method with the Morse potential as an example. This work shows that exact relativistic solutions can be a good starting point for obtaining nonrelativistic solutions even though a rigorous algebraic method is not found yet.

• Bulletin of the Korean Chemical Society
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• v.35 no.9
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• pp.2699-2703
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• 2014

We solve the Klein-Gordon equation with the modified Rosen-Morse potential energy model. The bound state energy equation has been obtained by using the supersymmetric shape invariance approach. The relativistic vibrational transition frequencies for the $6^1{\Pi}_u$ state of the $^7Li_2$ molecule have been computed by using the modified Rosen-Morse potential model. The calculated relativistic vibrational transition frequencies are in good agreement with the experimental RKR values.

• Bulletin of the Korean Chemical Society
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• v.7 no.1
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• pp.6-12
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• 1986

Overlap integrals for the case in which the ground and excited states are represented by Morse potential functions were derived. In order to calculate the spectral intensities in Morse wavefunctions, a method of expanding the wavefunctions of one state in terms of the other was developed to allow the ground and the excited state frequencies to be different. From the expansion of Morse wavefunctions, recursion formulas were developed for variational matrix elements of Morse wavefunctions. The matrix elements can be calculated using these recursion formulas and the diagonalized results which eigenvalues (allowed energies) were all successfully satisfied to Morse energy formulas.

• International Journal of Advanced Culture Technology
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• v.6 no.1
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• pp.42-49
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• 2018

In this study, we tried to reveal the state of stillness of Cho Ji-Hoon's poem "Silent Night 1" as a healing modifier. The language of poem is synaptically linked to the calmness emotion of the human body, seeking a principle that leads to a state of healing. Therefore, this study was carried out for the purpose of applying the principle to literary therapy program. The silent signal embedded in the poem is encoded into the signals of the sound as it is synapsed to the human body. Encoding of auditory nerves by poem lines is like a Morse code that word and word leave in the human body. The action potential of the auditory nerve is further activated by the potential difference between the word and the word represented by the neural network, such as a Morse code, which is accessed to the human body by such a path. There is worked as amplified potential difference between the words perceived by a sound which is synapsed to the human body and by a silence which is synapsed to the human body. The phenomenon of the words approaching the human body and setting the absence of sound and amplifying the sound is because the words amplifies the Morse codes in the human neural network. At this time, the signals overlap each other. Thereby this poem is increasing the amplitude of the sound. This overlapping of auditory signals appears and amplifies the catharsis. If this Cho Ji-Hoon Poem's principle is applied to literary therapy program in the future, more effective treatment will be done.

• Bulletin of the Korean Chemical Society
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• v.22 no.7
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• pp.721-726
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• 2001

The vibrational transition probability expressions for the forced Morse oscillator have been derived using the commutation relations of the anharmonic Boson operators. The formulation is based on the collinear collision model with the exponential repulsive potential in the framework of semiclassical collision dynamics. The sample calculation results for H2+ He collision system, where the anharmonicity is large, are in excellent agreement with those from an exact, numerical quantum mechanical study by Clark and Dickinson, using the reactance matrix. Our results, however, are markedly different from those of Ree, Kim and Shin's in which they approximate the commutation operator I。 as unity, the harmonic oscillator limit. We have concluded that the quantum number dependence in I。 must be retained to get accurate vibrational transition probabilities for the Morse oscillator.

• Korean Journal of Materials Research
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• v.1 no.2
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• pp.86-92
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• 1991

A potential energy function comprising a two-body potential term which is modified form Morse potential and a three-body potential term which is modified from Axilrod-Teller potential has been developed for small carbon clusters. The structural changes of small carbon clusters $C_2-C_6$ are qualitatively investigated by employing this potential energy function representing the energies of the small carbon cluster isotopes as a function of the three body intensity factor. It is found that the structure of the small carbon cluster changes from open structure to closed one, from complicated structure to simple one, and from three-dimensional structure to two-or-one dimensional one as the degree of the three-body interaction increases.