scholarly journals Erratum: Trial introduction of a complex potential function for perturbation that causes quantum mechanical transition in a one-dimensional harmonic oscillator, Mitsuru Yamada,International Journal of Quantum Chemistry (2004) 99(3) 127-141

2005 ◽  
Vol 102 (6) ◽  
pp. 1136-1138
Author(s):  
Mitsuru Yamada
Keyword(s):  
Quantum Chemistry ◽  
Harmonic Oscillator ◽  
Potential Function ◽  
Complex Potential ◽  
Quantum Mechanical ◽  
One Dimensional ◽  
Mechanical Transition

Eigenvalues of the Potential Function V=z4±Bz2 and the Effect of Sixth Power Terms

1970 ◽  
Vol 24 (1) ◽  
pp. 73-80 ◽  
Author(s):  
Jaan Laane
Keyword(s):  
Schrödinger Equation ◽  
Harmonic Oscillator ◽  
Potential Function ◽  
Schrodinger Equation ◽  
Harmonic Potential ◽  
Reduced Form ◽  
Approximation Formula ◽  
One Dimensional ◽  
Ring Puckering ◽  
The One

The one-dimensional Schrödinger equation in reduced form is solved for the potential function V = z4+ Bz2 where B may be positive or negative. The first 17 eigenvalues are reported for 58 values of B in the range −50⩽ B⩽100. The interval of B between the tabulated values is sufficiently small so that the eigenvalues for any B in this range can be found by interpolation. At the limits of the range of B the potential function approaches that of a harmonic oscillator with only small anharmonicity. The effect of a small Cz6 term on this potential is studied and it is concluded that a previously reported approximation formula is quite applicable but only for positive values of B. The success of the quartic—harmonic potential function for the analysis of the ring-puckering vibration is shown; it is also demonstrated that the same potential serves as a useful approximation for many other systems, especially those of the double minimum type.

scholarly journals The Harmonic Oscillator–A Simplified Approach

2008 ◽  
Vol 5 (3) ◽  
pp. 663-665
Author(s):  
L. R. Ganesan ◽  
M. Balaji
Keyword(s):  
Harmonic Oscillator ◽  
Infinite Series ◽  
Operator Method ◽  
Quantum Mechanical ◽  
Series Method ◽  
One Dimensional ◽  
Simplified Approach ◽  
Ladder Operator ◽  
Mechanical Methods ◽  
The One

Among the early problems in quantum chemistry, the one dimensional harmonic oscillator problem is an important one, providing a valuable exercise in the study of quantum mechanical methods. There are several approaches to this problem, the time honoured infinite series method, the ladder operator methodetc. A method which is much shorter, mathematically simpler is presented here.

scholarly journals TRANSITION AMPLITUDES WITHIN THE STOCHASTIC QUANTIZATION SCHEME

1994 ◽  
Vol 09 (32) ◽  
pp. 2953-2966 ◽  
Author(s):  
H. HÜFFEL ◽  
H. NAKAZATO
Keyword(s):  
Magnetic Field ◽  
Quantum Mechanics ◽  
Harmonic Oscillator ◽  
Constant Magnetic Field ◽  
Quantum Mechanical ◽  
Quantization Scheme ◽  
Stochastic Quantization ◽  
Nonrelativistic Particle ◽  
Mechanical Transition ◽  
Transition Amplitudes

Quantum mechanical transition amplitudes are calculated within the stochastic quantization scheme for the free nonrelativistic particle, the Harmonic oscillator and the nonrelativistic particle in a constant magnetic field; we conclude with free Grassmann quantum mechanics.

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