• 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.28 no.3
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• pp.408-412
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• 2007

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.

• Bulletin of the Korean Chemical Society
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• v.30 no.2
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• pp.315-318
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• 2009

Some particular bound state energies of an electron, under Coulomb potential field, confined in a two-dimensional circle and a three-dimensional sphere are analytically derived. The derivation shows that the electron cannot be bound in a negative energy state when the circle (or sphere) is smaller than a certain critical size. The critical size dependency on the strength of Coulomb potential and the angular momentum of the electron is also analytically derived. This system mimics quantum dots. Therefore the derivation provides new information on a minimum critical size of quantum dots with hydrogenic impurity.

• The Transactions of the Korean Institute of Electrical Engineers B
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• v.54 no.10
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• pp.483-491
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• 2005

To solve the 3D eddy current problems by using FE(finite element) method with MVP(magnetic vector potential) and electric scalar potential, Coulomb gauge condition and current continuity condition have to be considered. Coulomb gauge condition enforced on existing FE formulations to insure the uniqueness of MVP looks unnatural and current continuity condition which can be driven from Ampere's law looks unnecessary. So in this paper the effect of two conditions on FE formulations are investigated in order to help to obtain accurate numerical simulation results.

• Bulletin of the Korean Chemical Society
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• v.33 no.3
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• pp.818-824
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• 2012

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.

• Bulletin of the Korean Chemical Society
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• v.30 no.11
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• pp.2617-2620
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• 2009

Using Coulomb-Yukawa like correlated interaction potentials of integer and noninteger indices the series expansion formulae in terms of multicenter overlap integrals of three complete orthonormal sets of ${\psi}^{\alpha}$‒exponential type orbitals and linear combination coefficients of molecular orbitals are established for the potential of electrostatic field produced by the charges of molecule, where $\alpha$ = 1, 0, ‒1, ‒2,${\cdots}$. The formulae obtained can be useful for the study of interaction between atomic--molecular systems containing any number of closed and open shells when the ${\psi}^{\alpha}$‒exponential type basis functions and Coulomb-Yukawa like correlated interaction potentials are used in the Hartree-Fock-Roothaan and explicitly correlated approximations. The final results are valid for the arbitrary values of parameters of correlated interaction potentials and orbitals. As an example of application, the calculations have been performed for the potential energy of interaction between electron and molecule $H_2O$ using combined Hartree-Fock-Roothaan equations suggested by the author.

• Journal of Electrical Engineering and information Science
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• v.2 no.6
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• pp.208-211
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• 1997

We have fabricated a single-electron-tunneling(SET) transistor with a dual gate geometry based on the SOI structure prepared by SIMOX wafers. The split-gate is the lower-gate is the lower-level gate and located ∼ 100${\AA}$ right above the inversion layer 2DEG active channel, which yields strong carrier confinement with fully controllable tunneling potential barrier. The transistor is operating at low temperatures and exhibits the single electron tunneling behavior through nano-size quantum dot. The Coulomb-Blockade oscillation is demonstrated at 15mK and its periodicity of 16.4mV in the upper-gate voltage corresponds to the formation of quantum dots with a capacity of 9.7aF. For non-linear transport regime, Coulomb-staircases are clearly observed up to four current steps in the range of 100mV drain-source bias. The I-V characteristics near the zero-bias displays typical Coulomb-gap due to one-electron charging effect.

• Journal of the Korean Mathematical Society
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• v.44 no.5
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• pp.1065-1078
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• 2007

We consider initial value problems for the semirelativistic Hartree type equations with cubic convolution nonlinearity $F(u)=(V*{\mid}u{\mid}^2)u$. Here V is a sum of two Coulomb type potentials. Under a specified decay condition and a symmetric condition for the potential V we show the global existence and scattering of solutions.

• Bulletin of the Korean Chemical Society
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• v.10 no.6
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• pp.529-535
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• 1989

A general perturbation series solution of the Smoluchowski equation is applied to investigate the rate of recombination and the remaining probability of a pair of particles in liquids. The radiative boundary condition is employed and the convergence of the perturbation series is analyzed in terms of a convergene factor in time domain. The upper bound to the error introduced by the n-th order perturbation scheme is also evaluated. The long time behaviors of the rate of recombination and the remaining probability are found to be expressed in closed forms if the perturbation series is convergent. A new and efficient method of purely numerical integration of the Smoluchowski equation is proposed and its results are compared with those obtained by the perturbation method. For the two cases where the interaction between the particles is given by (i) the Coulomb potential and (ii) the shielded Coulomb potential, the agreement between the two results is found to be excellent.

• Bulletin of the Korean Chemical Society
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• v.13 no.3
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• pp.317-324
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• 1992

Structure and dynamics of $Na^+$ ions are investigated by molecular dynamics simulations of rigid dehydrated zeolite-A at several temperatures using a simple Lennard-Jones potential plus Coulomb potential. A best-fitted set of electrostatic charges is chosen from the results of simulation at 298.15 K and Ewald summation technique is used for the long-ranged character of Coulomb interaction. The calculated x, y, and z coordinates of $Na^+$ ions are in good agreement with the positions determined by X-ray crystallography within statistical errors, their random movings in different types of closed cages are well described by time-correlation functions, and $Na_Ⅰ$ type ions are found to be less diffusive than $Na_Ⅱ$ and $Na_{III}$. At 600.0 K, the unstable $Na_{III}$ type ion pushes down one of nearest $Na_{I}$ ions into the $\beta-cage$ and sits on the stable site Ⅰ, and the captured ion in the $\beta-cage$ wanders over and attacks one of 8 $Na_{I}$ type ions.