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The Schrödinger wave equation cannot be derived (at least not by any known means). Erwin Schrödinger literally guessed the equation (though his guess had reason behind it), and justification for its use can be attributed to the simple fact that it works.
Thought it was guess when Schrödinger formulated his wave equation he drew from a classical foundation. Total energy is equal to the kinetic energy plus the potential energy. Classically kinetic energy is expressed as p2/(2m), where p is momentum and m is the mass. The potential can be whatever you want it to be so we will just call it V, then finally lets call the total energy E. We put this all together to get p2/(2m)+V=E but in terms of operators p=[i*h/(2*pi)]*(d2/dqi2), where i is the square root of negative one, h is Planck's constant, pi is 3.141529, and (d2/dqi2) is the second order differential with respect to space in generalized coordinates. So putting p back in our equation for energy we get [- h2/(4*pi*m)]*(d2/dqi2)+V=E. Now comes the sort of complex part. In general the total energy of a system is defined by the Hamiltonian, lets call is H. Now, E is the eigenvalue of the Hamiltonian operator. Meaning that when H operates on some state it is measuring the total energy of that state. In quantum mechanics H=[i*h/(2*pi)]*(d/dt), where (d\dt) is the first order differential with respect to time. Now putting this all together we get [i*h/(2*pi)]*(d/dt)=[- h2/(4*pi*m)]*(d2/dqi2)+V. That, to me, is Schrodinger's "picture" of the wave equation.
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Sorry it is a bit lengthy but I wanted to be thorough.
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What are the differences in the use of the time-dependent Schrodinger equation and the time-independent Schrodinger equation?
The time-independent Schr
What is the importance of boundary conditions in solving the schrodinger's wave equation?
Boundary conditions allow to determine constants involved in the equation. They are basically the same thing as initial conditions in Newton's mechanics (actually they are initial conditions).
Who designed a mathematical equation for the model of the atom?
Erwin Schrodinger
What is clausius mossotti equation?
derive clausious mossotti equation
Solution of maxwell equation in the form of wave equation?
Yes it is
When was the electron wave equation written?
This is the Schrodinger equation from 1925-1926.
Shapes of electron orbital are determined by what equations?
Schrodinger wave equation
How did heisenberg's principle influence schrodinger to develop his wave equation?
Heisenberg's uncertainty principle, which states the limitations in simultaneously measuring a particle's position and momentum accurately, inspired Schrodinger to find a description of particles in terms of waves. This led Schrodinger to develop his wave equation, which describes the behavior of quantum particles in terms of wave functions.
Derive schrodinger wave equation?
The Schrödinger wave equation describes how the quantum state of a system evolves over time. It is obtained by applying the principles of quantum mechanics to a system's wave function, resulting in a differential equation that describes how the wave function changes in time. The equation is named after physicist Erwin Schrödinger who originally formulated it in 1926.
Why quantum mechanics is someone called wave mechanics?
It is also called wave mechanics because quantum mechanics governed by Schrodinger's wave equation in it's wave-formulation.
How Heisenberg's principle influenced Schrodinger to develop his wave equation?
Heisenberg's Uncertainty Principle introduced the concept of inherent uncertainty in measuring both the position and momentum of a particle simultaneously. This influenced Schrodinger to develop a wave equation that could describe the behavior of particles in terms of probability waves rather than definite trajectories, allowing for a more complete description of quantum systems. Schrodinger's wave equation provided a way to predict the behavior of quantum particles without violating the Uncertainty Principle.
How did Erwin Schrodinger achieve quantum mechanics?
Erwin Schrodinger developed a wave equation, known as the Schrodinger equation, that describes how the quantum state of a physical system changes over time. This equation is a fundamental tool in quantum mechanics, providing a mathematical framework for predicting the behavior of particles at the quantum level. Schrodinger's work was crucial in the development of quantum mechanics as a coherent and successful theory.
Who created the wave?
Schrodinger
The atom of Erwin Schrodinger and Louis de B oglie?
Erwin Schrodinger is known for his Schrodinger equation, which describes how the wave function of a physical system changes over time. Louis de Broglie proposed the concept of wave-particle duality, suggesting that particles like electrons can exhibit wave-like properties. Both of these contributions were instrumental in the development of quantum mechanics.
What are the differences in the use of the time-dependent Schrodinger equation and the time-independent Schrodinger equation?
The time-independent Schr
Can we apply schrodinger's wave equation to a particle having velocity comparable with the velocity of the light?
Schrodinger's wave equation does not accurately describe the behavior of particles with velocities comparable to the speed of light. In this case, relativistic quantum mechanics, specifically the Dirac equation, is needed to properly describe the behavior of particles moving at relativistic speeds. The Dirac equation incorporates special relativity and provides a more accurate description of such high-speed particles.
Which scientist was able to determine the electronic structure of the atom using an equation known as the quantum model that included the wave nature of the electron?
Erwin Schrodinger
