An approach to the calculation of the wavelet function using the Schrödinger equation for the harmonic oscillator
Subject Areas : MAth Education
1 - Department of Physics, Kermanshah Branch, Islamic Azad University, Kermanshah, Iran
Keywords: تبدیل فوریه زمان کوتاه, حالت های همدوس, تبدیل فوریه, تبدیل موجک, عدم قطعیت,
Abstract :
The concept of probability and uncertainty has always been considered a fundamental principle in quantum physics. One of the most important results of this principle is the particle properties of radiation and the wave properties of matter. In quantum physics, the particle wave function can be explained using the mathematical formalism of the Fourier transform. Based on the qualitative observations that occur in the wave discussion, the inversion pattern of the widths is always established in the two spaces of position and momentum. Such a property is a property of all functions that are Fourier transforms of each other. One of the problems is that the Fourier transform determines whether there is a certain frequency in the wave or not and it does not give information about where this frequency is located in the wave. The problems facing the Fourier transform led to the creation of the Short-time Fourier transform, which also faces problems due to the Heisenberg uncertainty principle. In contrast to the short-time Fourier transform, there are other types of transforms known as wavelet transforms. Using the wavelet transform has the advantage over the Fourier transform that it reduces the uncertainty in the measurements to a smaller amount. In this paper, using the solutions of the Schrödinger equation for the quantum oscillator, the translation operator and Hermitian polynomials, a method to obtain a type of wavelet is presented.
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