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Position Dependent Mass for the Hulth´ en plus Hyperbolic Cotangent Potential

Sanjib Meyur, Rabindra Sarani

Exactly solvable Schrodinger equations with a position-dependent mass are proposed. Nikiforov-Uvarov method is used to obtain the energy eigenvalues and the corresponding wavefunctions.

Jan 1, 20110 citations

Particle in a Box: Quantisation of Translational Energy

Amita Dua

The motion and all the properties of a particle of mass ‘ m ’ which moves with potential energy, V ( x, y, z ) can be obtained from solution of well behaved fundamental Schrödinger wave equation https://www.w3.org/1998/Math/MathML" display="block"> − ℏ 2 2 m ∇ 2 ψ + V ( x , y , z ) ψ = E ψ

CRC Press eBooksNov 6, 20250 citations

The Solution of Quantum Particle-Wave Duality

Mirosław Kozłowski, Janina Marciak-kozlowska B

In this essay, we discuss the enigma of quantum particle-quantum wave duality. We find new interpretation our hyperbolic Schrodinger equation (HSE). This equation describes simul-taneously Bohm wave which propagates with c-light velocity and is independent of mass of particle m i and Schrodinger equation . M P is the mass of Planck particle.

Journal of consciousness exploration & researchJan 18, 20200 citations

The Schrödinger Equation

Muhammad Suhail Zubairy

In this chapter, the Schrödinger equation is “derived” for particles that can be described by de Broglie waves. The Schrödinger equation is very different from the corresponding equation of motion in classical mechanics. In order to illustrate the fundamental differences between the two theories, one of the simplest problems of particle dynamics is solved in both Newtonian and quantum mechanics. This simple example also helps to show that quantum mechanics is the fundamental theory and classical mechanics is an approximation, a remarkably good approximation, when considering macroscopic objects. The solution of the Schrödinger equation is presented for a particle inside a box and the quantization condition is derived. The amazing possibility of quantum tunneling when a particle is incident on a barrier of height larger than the energy of the incident particle is also discussed. Finally the three-dimensional Schrödinger equation is solved for the hydrogen atom.In this chapter, the Schrödinger equation is “derived” for particles that can be described by de Broglie waves. The Schrödinger equation is very different from the corresponding equation of motion in classical mechanics. In order to illustrate the fundamental differences between the two theories, one of the simplest problems of particle dynamics is solved in both Newtonian and quantum mechanics. This simple example also helps to show that quantum mechanics is the fundamental theory and classical mechanics is an approximation, a remarkably good approximation, when considering macroscopic objects. The solution of the Schrödinger equation is presented for a particle inside a box and the quantization condition is derived. The amazing possibility of quantum tunneling when a particle is incident on a barrier of height larger than the energy of the incident particle is also discussed. Finally the three-dimensional Schrödinger equation is solved for the hydrogen atom.

Oxford University Press eBooksMay 7, 20200 citations

Particle in a Box: Quantisation of Translational Energy

Amita Dua, Chayannika Singh

All the properties and motion of a particle of mass ‘ m ’ which moves with potential energy, V ( x, y, z ) can be obtained from solution of well behaved Schrodinger equation https://www.w3.org/1998/Math/MathML" display="block"> − ħ 2 2 m ∇ 2 ψ + V ( x , y , z ) ψ = E ψ https://www.w3.org/1999/xlink" content-type="black-white" xlink:href=" https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003490135/247a5333-15ea-46ba-8a55-ecb37a472373/content/math4-1_B.tif "/>All the properties and motion of a particle of mass ‘ m ’ which moves with potential energy, V ( x, y, z ) can be obtained from solution of well behaved Schrodinger equation https://www.w3.org/1998/Math/MathML" display="block"> − ħ 2 2 m ∇ 2 ψ + V ( x , y , z ) ψ = E ψ https://www.w3.org/1999/xlink" content-type="black-white" xlink:href=" https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003490135/247a5333-15ea-46ba-8a55-ecb37a472373/content/math4-1_B.tif "/>

CRC Press eBooksMar 15, 20240 citations

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, 20210 citations

Schrodinger equation for classical particles

Abstract

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Schrodinger equation for classical particles

Abstract

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