Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Momentum And Group Velocity As A Function Of The Wavefunction Assuming a time independent Schrödinger equation, this paper shows the formulas for the wavelength, momentum and group velocity of a particle as a function of its wavefunction.

Rodolfo A. Frino

Published Jan 1, 2015• 0 citations
OpenAlex

Related papers

Momentum And Group Velocity As A Function Of The Wavefunction

Rodolfo A. Frino

Assuming a time independent Schrodinger equation, this paper shows the formulas for the wavelength, momentum and group velocity of a particle as a function of its wavefunction.

•Dec 1, 2015•0 citations

Phase Velocity And Group Velocity For Beginners

Rodolfo A. Frino

In the first section of this paper I derive the formulas for the phase velocity and group velocity as a function of the total relativistic energy and the momentum of a particle. In the second section I derive similar formulas as a function of the de Broglie and the Compton wavelengths of the particle. In the third section, I derive similar formulas as a function of the angular frequency and the wave number. Finally, two additional meanings of the Compton wavelength are derived. The first one is derived from the equation of the group velocity in terms of the de Broglie and the Compton wavelengths and the second one from the range of the weak nuclear force.

•Jan 1, 2015•1 citation

Schrodinger Equation and Free Particle Wave Function

Karl De Paepe

Using the wave function of a free particle we obtain a solution of the Schrodinger equation for a class of potentials.

•Jan 1, 2021•0 citations

A class of traveling-envelope solutions of free Schrödinger equation generated by Lorentz transformation

Agus Budiyono

We develop a class of traveling-envelope solutions of Schrödinger equation for a free particle whose amplitude is moving with constant group velocity while keeping its shape undistorted. We show that solution with arbitrary finite group velocity is obtained by Lorentz boosting the solution with vanishing group velocity, if the quantum average energy $E$ and momentum $p$ are related to the rest-mass $m$ of the particle by Einstein formula $E^2/c^2-p^2=m^2c^2$. The wave function is spatially localized with finite-size support which is decreasing as the rest-mass and/or group velocity are increased. For a particle with vanishing rest-mass yet finite momentum, we show that the group and phase velocities are equal to the velocity of light and the wavelength is given by Einstein another formula $λ_P=h/p$.

arXiv:physics/0609216•Sep 24, 2006•0 citations

A General Solution of the Schrödinger Equation

The wave equation in quantum mechanics and its general solution in the phase space are obtained.

WORLD SCIENTIFIC eBooks•Aug 1, 2020•0 citations

The Schrodinger Wave Equation

Vinod Kumar Khanna

Time-independent and time-dependent forms of Schrodinger equations are presented in one and three dimensions along with their interpretations. Also, the time-independent version is shown to follow from the time-dependent version. For better conceptualization of wave motion, the general equation of wave motion is discussed and solved, explaining the physical significance of variables involved. Born interpretation of the wave function as a measure of the probability of finding the particle in a region of space at a given instant is described. The requirements to be fulfilled by the wave function for representing a physical world system are outlined.

CRC Press eBooks•Jun 30, 2020•0 citations
In the first section of this paper I derive the formulas for the phase velocity and group velocity as a function of the total relativistic energy and the momentum of a particle. In the second section I derive similar formulas as a function of the de Broglie and the Compton wavelengths of the particle. In the third section, I derive similar formulas as a function of the angular frequency and the wave number. Finally, two additional meanings of the Compton wavelength are derived. The first one is derived from the equation of the group velocity in terms of the de Broglie and the Compton wavelengths and the second one from the range of the weak nuclear force.
We develop a class of traveling-envelope solutions of Schrödinger equation for a free particle whose amplitude is moving with constant group velocity while keeping its shape undistorted. We show that solution with arbitrary finite group velocity is obtained by Lorentz boosting the solution with vanishing group velocity, if the quantum average energy EEE and momentum ppp are related to the rest-mass mmm of the particle by Einstein formula E2/c2−p2=m2c2E^2/c^2-p^2=m^2c^2E2/c2−p2=m2c2. The wave function is spatially localized with finite-size support which is decreasing as the rest-mass and/or group velocity are increased. For a particle with vanishing rest-mass yet finite momentum, we show that the group and phase velocities are equal to the velocity of light and the wavelength is given by Einstein another formula λP=h/pλ_P=h/pλP​=h/p.
Time-independent and time-dependent forms of Schrodinger equations are presented in one and three dimensions along with their interpretations. Also, the time-independent version is shown to follow from the time-dependent version. For better conceptualization of wave motion, the general equation of wave motion is discussed and solved, explaining the physical significance of variables involved. Born interpretation of the wave function as a measure of the probability of finding the particle in a region of space at a given instant is described. The requirements to be fulfilled by the wave function for representing a physical world system are outlined.