Wave Function Wave Function A Wave Function can be defined as a probability amplitude which is given in quantum mechanics, to define quantum state of a particle and see how the particle behave. Generally complex numbers are taken for the wave function values. Wave function can be represented by the symbol 'ψ'. Either ψ (wave function) is a complex number, |ψ|2 (wave function square) is real, and corresponding to the probability density of calculating a particle in a given place at a particular given time. The SI unit is defined for ψ is totally depend upon the system. In three dimensional for one particle, the SI unit is given as m-3/2. For the different number of particles such as and/or dimensions, the SI unit of wave function is different. It can be calculating by dimensional analysis. Generally the wave function is defined for central to quantum mechanics. Now we will see the mathematical introduction of wave function.In mathematics, Multi-variable calculus and analysis are used to identification of wave function in the given number of situations. Let's understood some of the points to formalism this situations.

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At each position and time coordinate, the probability amplitude is having a value by direct calculation. Functions also define the wave – like motion by using the periodic functions and the Fourier can be easily done. Here functions are very easy to obtained, visualize and interpret because of the nature of the function graph. If the situations is in high number than the dimensions. It is also possible to analysis the function in the lower dimensions. Now we will discuss some of the properties of wave function. The properties of wave function is shown below: As we know that the wave function is represented by the symbol 'ψ'. 'ψ' – It contain all the information that is measurable about the given particle. 'ψ' – ψ *ψ sum of all the space is equal to 1( if the particle exists, or the probability of calculating the wave function is somewhere must be one) 'ψ' – it is continuous in nature of physics. 'ψ'- It is used to solve the energy calculation using the schrodinger equation. 'ψ' – The wave function is also used to establish a probability distribution in the three dimensional space. 'ψ' – It allow the calculation of the effective average value (or we can say the exception value) of a given variable. 'ψ' – It is also used to find the momentum and total uncertainty position. Let's discuss the basic requirement for the wave function.

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The wave function is finite everywhere (or its value is always finite). It is also continuous function and continuously differentiable everywhere. As a corollary wave function, the function value should be single- valued otherwise the multiple probabilities occur at the same position and time. Wave function is also satisfy the normalization condition everywhere so that the particle exist with 100 percent certainty. If all these requirements of wave function are not correct then it is not possible to interpret the wave function as a probability amplitude. Then the value of wave function and the first order derivative may not be finite and definite. In mathematics, the probability of wave function can be infinite or multivalued at any of the one position and time. This is all about the wave function.

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