QUANTUM TIME DILATION: RELATION BETWEEN TIME DILATION AND ENERGY DIFFERENCE OF QUANTUM WAVE FUNCTIONS IN GALILEAN AND LORENTZ FRAMES

Tanujit Mondal; Hriddhiman Bag; Arnab Maitra

doi:10.30574/ijsra.2026.20.3.1779

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QUANTUM TIME DILATION: RELATION BETWEEN TIME DILATION AND ENERGY DIFFERENCE OF QUANTUM WAVE FUNCTIONS IN GALILEAN AND LORENTZ FRAMES

Tanujit Mondal ^{1, *}, Hriddhiman Bag ¹ and Arnab Maitra ²

¹ M. Tech Scholar, Department of Civil Engineering, NITTTR Kolkata, PIN - 700106
² M. Tech, Artificial Intelligence & Machine Learning, NITTTR Kolkata, PIN - 700106
* Corresponding Author

Research Article

International Journal of Science and Research Archive, 2026, 20(03), 544–548

Article DOI: 10.30574/ijsra.2026.20.3.1779

DOI url: https://doi.org/10.30574/ijsra.2026.20.3.1779

Publication history

Received on 02 August 2026; revised on 13 September 2026; accepted on 16 September 2026

Abstract

This paper investigates the quantum mechanical relationship between time dilation and energy difference of the quantum photon and electron wave functions. The wave functions are studied under two different times and and two energy differences and . The time-dependent Schrödinger equation (TDSE) is used to analyse the wave functions and time dilation is studied in the Galilean frame of reference. A key relation linking Lorentz time dilation to the energy difference between the photon (relativistic kinetic energy) and electron (classical kinetic energy) wave functions is derived analytically. Python simulation is used to compute and visualise the wave function phase, energy ratio, total phase energy, and time dilation as functions of speed v/c.

Keywords

Quantum Wave Function, Time Dilation, Schrödinger Equation, Galilean Frame, Lorentz Transformation, Photon, Electron, Energy Difference, Relativistic Kinetic Energy

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How to cite this article

Tanujit Mondal, Hriddhiman Bag and Arnab Maitra. QUANTUM TIME DILATION: RELATION BETWEEN TIME DILATION AND ENERGY DIFFERENCE OF QUANTUM WAVE FUNCTIONS IN GALILEAN AND LORENTZ FRAMES. International Journal of Science and Research Archive, 2026, 20(03), 544–548. Article DOI: https://doi.org/10.30574/ijsra.2026.20.3.1779.

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