On quantum harmonic oscillator being subjected to absolute potential state

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• 作者：SWAMI NITYAYOGANANDA
• 关键词：Quantum harmonic oscillator ; like ; potential energy ; wave function ; energy density
• 刊名：Pramana
• 出版年：2017
• 出版时间：January 2017
• 年：2017
• 卷：88
• 期：1
• 全文大小：
• 刊物类别：Physics and Astronomy
• 刊物主题：Physics, general; Astronomy, Observations and Techniques; Astrophysics and Astroparticles;
• 出版者：Springer India
• ISSN：0973-7111
• 卷排序：88

文摘

In a quantum harmonic oscillator (QHO), the energy of the oscillator increases with increased frequency. In this paper, assuming a boundary condition that the product of momentum and position, or the product of energy density and position remains constant in the QHO, it is established that a particle subjected to increasing frequencies becomes gradually subtler to transform into a very high dormant potential energy. This very high dormant potential energy is referred to as ‘like-potential’ energy in this paper. In the process a new wave function is generated. This new function, which corresponds to new sets of particles, has scope to raise the quantum oscillator energy (QOE) up to infinity. It is proposed to show that this high energy does not get cancelled but remains dormant. Further, it is proposed that the displacement about the equilibrium goes to zero when the vibration of the oscillator stops and then the QOE becomes infinity – this needs further research. The more the QOE, the greater will be the degree of dormancy. A simple mathematical model has been derived here to discuss the possibilities that are involved in the QHO under the above-mentioned boundary conditions.