What is wave function and what are its properties?
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A wave function in quantum physics is a mathematical description of the quantum state of an isolated quantum system.
The Schrödinger equation is an equation of quantum mechanics: calculated wave functions have discrete, allowed values for electrons bound in atoms and molecules; all other values are forbidden. In addition to the importance of Ψ, its square Ψ2 also has enormous significance in chemistry. Ψ2 is the probability density.
The wavefunction for any particle with well-defined momentum, as ours has, cannot be purely real. This results from the eigenvalue equation:
, (12)
where p is always real as it represents the actual momentum of the particle. As a result if is real, would be real but would be purely imaginary, and so they cannot be equal.
When the particle beam meets a potential barrier there will be terms in the wavefunction that describe incident and reflected fluxes of particles, similar to light when it hits the interface between media of different refractive indices.
is the probability density of finding a particle in a particular volume. It is difficult to normalise the wavefunction of a plane wave travelling in a constant potential, as the solution extends from so the integral of over all space has to be infinite. This problem can be overcome by saying that the travelling wave describes a beam of particles moving with the same velocity, and the amplitude of the wave specifies the number of particles in the beam. If is the speed of each particle passing a point in a second then the v is number in length v. This means that the particle current is particles per second.
The Schrödinger equation is an equation of quantum mechanics: calculated wave functions have discrete, allowed values for electrons bound in atoms and molecules; all other values are forbidden. In addition to the importance of Ψ, its square Ψ2 also has enormous significance in chemistry. Ψ2 is the probability density.
The wavefunction for any particle with well-defined momentum, as ours has, cannot be purely real. This results from the eigenvalue equation:
, (12)
where p is always real as it represents the actual momentum of the particle. As a result if is real, would be real but would be purely imaginary, and so they cannot be equal.
When the particle beam meets a potential barrier there will be terms in the wavefunction that describe incident and reflected fluxes of particles, similar to light when it hits the interface between media of different refractive indices.
is the probability density of finding a particle in a particular volume. It is difficult to normalise the wavefunction of a plane wave travelling in a constant potential, as the solution extends from so the integral of over all space has to be infinite. This problem can be overcome by saying that the travelling wave describes a beam of particles moving with the same velocity, and the amplitude of the wave specifies the number of particles in the beam. If is the speed of each particle passing a point in a second then the v is number in length v. This means that the particle current is particles per second.
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