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What are symmetric and antisymmetric wave-functions

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apniPhysics

visit http://www.apniphysics.com for physics video lectures...........wave function have no physical significance its just a mathematical quantity.....a function that depends on coordinates x,y and z in a space.....time t is also a factor but in terms of position here not required....if you change the...
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visit http://www.apniphysics.com for physics video lectures...........wave function have no physical significance its just a mathematical quantity.....a function that depends on coordinates x,y and z in a space.....time t is also a factor but in terms of position here not required....if you change the position of coordinates means from x to -x or from y to -y does you observe any change in the property of the function and ultimately in the probability of finding the particle. Mathematically if there is no change symmetric if you notice change in sign obvious that will be asymmetric.... read less
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Identical particles and multielectron atoms undergo a change of sign; the change of sign is permitted because it is ?2 that occurs in the physical interpretation of the wave function. If the sign of ? remains unchanged, the wave function is said to be symmetric with respect to interchange; if the sign...
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Identical particles and multielectron atoms undergo a change of sign; the change of sign is permitted because it is ?2 that occurs in the physical interpretation of the wave function. If the sign of ? remains unchanged, the wave function is said to be symmetric with respect to interchange; if the sign changes, the function is antisymmetric. read less
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We have to construct the wave function for a system of identical particles so that it reflects the requirement that the particles are indistinguishable from each other. Mathematically, this means interchanging the particles occupying any pair of states should not change the probability density of the...
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We have to construct the wave function for a system of identical particles so that it reflects the requirement that the particles are indistinguishable from each other. Mathematically, this means interchanging the particles occupying any pair of states should not change the probability density of the system. This simple statement has the enormous consequence of dividing all particles in nature into one of two classes. An example for two non-interacting identical particles will illustrate the point. The probability density of the the two particle wave function $\Psi(\bf {r}_1, \bf {r}_2)$ must be identical to that of the the wave function $\Psi(\bf {r}_2, \bf {r}_1)$ where the particles have been interchanged. \vert\Psi({\bf r}_1, {\bf r}_2)\vert^2 = \vert\Psi({\bf r}_2, {\bf r}_1)\vert^2 We can achieve this in two ways {Symmetric case : \ \ \ }\Psi({\bf r}_1, {\bf r}_2) = \Psi({\bf r}_2, {\bf r}_1) or {Anti-symmetric case : \ \ \ }\Psi({\bf r}_1, {\bf r}_2) = -\Psi({\bf r}_2, {\bf r}_1) read less
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