Abstract
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.
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Acknowledgements
The author’s first and foremost acknowledgement is due to the Ramakrishna Math and Ramakrishna Mission – the twin organizations where he belongs. This spiritual organization is well known for preserving ancient Indian tradition coupled with modern scientific knowledge – as envisaged by Swami Vivekananda. This unique environment in the organization paved the way for the development and completion of this paper.
The research has been greatly aided with the support of Dr J Vasundhara Devi, Professor, Associate Director, Lakshmikantham Institute for Advanced Studies –Gayatri Vidya Parishad College of Engineering (GVP-LIAS), Visakhapatnam. She has extensively helped to bring this paper to a proper readable shape.
The contribution of Prof. Seetapathi, Retired Professor, Department of Applied Mathematics, Andhra University is also thankfully acknowledged. He diligently studied the mathematical derivations in the paper and made valuable suggestions and corrections wherever needed.
The invaluable support extended by Dr T G K Murty, former Program Director, ISRO, and an outstanding scientist, Bangalore, is also duly acknowledged here. His constant guidance, encouragement and his valuable insights at proper time provided a meaningful direction to the paper.
Acknowledgement is further due to Mr D Ammaji Rao, Student, Andhra University. He made many appropriate suggestions with regard to the MATLAB plots and the mathematical part of this paper.
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NITYAYOGANANDA, S. On quantum harmonic oscillator being subjected to absolute potential state. Pramana - J Phys 88, 4 (2017). https://doi.org/10.1007/s12043-016-1311-x
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DOI: https://doi.org/10.1007/s12043-016-1311-x