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Exactly Solvable Potentials Derived from SWKB Quantization
선호성 대한화학회 2014 Bulletin of the Korean Chemical Society Vol.35 No.3
The shape invariant potentials are proved to be exactly solvable, i.e. the wave functions and energies of a particle moving under the influence of the shape invariant potentials can be algebraically determined without any approximations. It is well known that the SWKB quantization is exact for all shape invariant potentials though the SWKB quantization itself is approximate. This mystery has not been mathematically resolved yet and may not be solved in a concrete fashion even in the future. Therefore, in the present work, to understand (not prove) the mystery an attempt of deriving exactly solvable potentials directly from the SWKB quantization has been made. And it turns out that all the derived potentials are shape invariant. It implicitly explains why the SWKB quantization is exact for all known shape invariant potentials. Though any new potential has not been found in this study, this brute-force derivation of potentials helps one understand the characteristics of shape invariant potentials.
General Orthogonality for Orthogonal Polynomials
선호성 대한화학회 2013 Bulletin of the Korean Chemical Society Vol.34 No.1
The bound state wave functions for all the known exactly solvable potentials can be expressed in terms of orthogonal polynomials because the polynomials always satisfy the boundary conditions with a proper weight function. The orthogonality of polynomials is of great importance because the orthogonality characterizes the wave functions and consequently the quantum system. Though the orthogonality of orthogonal polynomials has been known for hundred years, the known orthogonality is found to be inadequate for polynomials appearing in some exactly solvable potentials, for example, Ginocchio potential. For those potentials a more general orthogonality is defined and algebraically derived. It is found that the general orthogonality is valid with a certain constraint and the constraint is very useful in understanding the system.
The Analytical Transfer Matrix Method Combined with Supersymmetry: Coulomb Potential
선호성 대한화학회 2007 Bulletin of the Korean Chemical Society Vol.28 No.3
Combining the analytical transfer matrix method with supersymmetry algebra, a new quantization condition is suggested. To demonstrate the efficiency of the new quantization condition, the eigenenergies of the Coulomb potential are analytically derived. The scattering-led phase shifts are also determined and they are the same for all Coulomb potential states. It is found that the new quantization condition is mathematically simple and exact.
Quantization Rule for Relativistic Klein-Gordon Equation
선호성 대한화학회 2011 Bulletin of the Korean Chemical Society Vol.32 No.12
Based on the exact quantization rule for the nonrelativistic Schrödinger equation, the exact quantization rule for the relativistic one-dimensional Klein-Gordon equation is suggested. Using the new quantization rule, the exact relativistic energies for exactly solvable potentials, e.g. harmonic oscillator, Morse, and Rosen-Morse II type potentials, are obtained. Consequently the new quantization rule is found to be exact for one-dimensional spinless relativistic quantum systems. Though the physical meanings of the new quantization rule have not been fully understood yet, the present formal derivation scheme may shed light on understanding relativistic quantum systems more deeply.
Nonrelativistic Solutions of Morse Potential from Relativistic Klein-Gordon Equation
선호성 대한화학회 2010 Bulletin of the Korean Chemical Society Vol.31 No.12
Recently it is suggested that it may be possible to obtain the approximate or exact bound state solutions of nonrelativistic Schrödinger 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.
Langer Modification in WKB Quantization for Translationally Shape Invariant Potentials
선호성 대한화학회 2012 Bulletin of the Korean Chemical Society Vol.33 No.3
When the Langer modification is applied to Coulomb potential, the standard WKB quantization yields an exact energy spectrum for the potential. This Langer modification has been known to be related to the centrifugal term appearing in Coulomb potential. But we find that a similar modification exists for all translationally shape invariant potentials without referring to the centrifugal term. The characteristic shape of the potentials accounts for the generalized version of Langer modification that makes the WKB quantization valid for all translationally shape invariant potentials.
선호성,이춘실,Sun Yeoul Lee 대한화학회 2008 Bulletin of the Korean Chemical Society Vol.29 No.2
The physical chemistry (PC) articles published in the Bulletin of the Korean Chemical Society (BKCS) from 2003 to 2007 are surveyed, and in-depth content analysis was conducted to classify the PC articles into 12 topics used in The Journal of Physical Chemistry (JPC). The PC articles published in the Journal of the American Chemical Society (JACS) in 2007 are also surveyed. The extensive summary of all PC articles in BKCS for the last five years reveals the current trend of physical chemistry research in Korea. The comparison study with the JACS shows that the proportion of PC articles among all articles published in BKCS (16%) is slightly higher than that of JACS (11%), and the non-Korean authorship ratio of BKCS (12%) is very low compared with the non-US authorship of JACS (52%). From the comparison study with articles published in JPC in 2007, it is found that BKCS disseminates various topics of physical chemistry researches adequately. In particular, BKCS most frequently published PC articles in molecular structure and spectroscopy topics, whereas JPC published surface chemistry and nano-chemistry articles most frequently. It is concluded that BKCS should publish more articles to be a leading journal, and it is suggested that the SCI impact factor of BKCS must be increased by improving the electronic version of BKCS.
선호성 대한화학회 2008 Bulletin of the Korean Chemical Society Vol.29 No.1
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.
Widths and Positions of Isolated Resonances in the Predissociation of SH:Quantal Treatments
이성율,선호성,Lee, Seong Yul,Seon, Ho Seong Korean Chemical Society 2001 Bulletin of the Korean Chemical Society Vol.22 No.2
The predissociating resonances are treated for the SH molecule by quantal method. The isolated resonances (N'=0, v' = 0-6) are predicted to be highly Lorentzian. The widths and positions of the isolated resonances are computed as functions of v'. The magnitudes and signs of the widths and the shifts as functions of v' are discussed in terms of the distance of the resonance from the crossing points between the bound state (A 2Σ+ ) and the repulsive states ( 4Σ- , 2Σ- and 4Π).