What is Schrodinger wave equation ?
Schrodinger, gave a wave equation to describe the wave behaviour of electrons in atoms and molecules, called Schrodinger wave equation.
The Schrodinger wave equation for an electron wave propagating in three dimensions in space, is written as follows.
Where, m = mass of electron, h = plank`s constant, E = total energy of electron,
V = electrostatic potential energy and Ψ = wave function.
What is the significance of wave equation ?
The Schrodinger wave equation is a second order differential equation.It has countless solutions., many of them having no significance.
Out of these, only those solutions are significant which give certain definite and acceptable values of the total energy E.
The acceptable values of the total energy E of wave particle given by a solution is called eigen value and the corresponding function Ψ which gives eigen value of the energy, is called eigen function.
The wave function Ψ in Schrodinger wave equation, has no physical significance except than it represents the amplitude of the electron wave.
However, the square of the wave function ,that is, Ψ2 gives the probability of an electron of a given energy E, from place to place in a given region around the nucleus.
It is thus possible to identify regions of space around the nucleus where there is high probability of locating an electron associated with a specific energy. This space is called an atomic orbital.
An atomic orbital,thus represents a definite region in three dimensional space around the nucleus where there is high probability of finding an electron of a specific energy E.
An acceptable solution of Schrodinger wave equation, that is, an eigen wave function ,must satisfy the following conditions.
1.The function should be finite.
2.It should be single valued, that is, it should not have more than one value at a point in space.
3. It should be continuous ,that is, the function if plotted in space should not show a break.
Out of these, only those solutions are significant which give certain definite and acceptable values of the total energy E.
The acceptable values of the total energy E of wave particle given by a solution is called eigen value and the corresponding function Ψ which gives eigen value of the energy, is called eigen function.
The wave function Ψ in Schrodinger wave equation, has no physical significance except than it represents the amplitude of the electron wave.
However, the square of the wave function ,that is, Ψ2 gives the probability of an electron of a given energy E, from place to place in a given region around the nucleus.
It is thus possible to identify regions of space around the nucleus where there is high probability of locating an electron associated with a specific energy. This space is called an atomic orbital.
An atomic orbital,thus represents a definite region in three dimensional space around the nucleus where there is high probability of finding an electron of a specific energy E.
An acceptable solution of Schrodinger wave equation, that is, an eigen wave function ,must satisfy the following conditions.
1.The function should be finite.
2.It should be single valued, that is, it should not have more than one value at a point in space.
3. It should be continuous ,that is, the function if plotted in space should not show a break.
5.The function should be normalised,that is,
This is the significance of Schrodinger wave equation in quantum mechanics.
This is the significance of Schrodinger wave equation in quantum mechanics.
What is the significance of wave function?
The wave function Ψ in Schrodinger wave equation, has no physical significance except than it represents the amplitude of the electron wave.
However, the square of the wave function ,that is, Ψ2 gives the probability of an electron of a given energy E, from place to place in a given region around the nucleus .
It is thus possible to identify regions of space around the nucleus where there is high probability of locating an electron associated with a specific energy. This space is called an atomic orbital.
Practice problems
- What is Schrodinger wave
equation ?
- What is the significance
of wave function?
- What is atomic orbital
?
- What is Schrodinger wave equation ?
- What is the significance of wave function?
- What is atomic orbital ?
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