My textbook( A Textbook of Physical Chemistry, Dr. O.P. Tandon ) says that solution of the Schrödinger's wave equation exists only for certain permissible values which are called eigen values.( physically possible ones).

How to determine the permissible solutions of the wave equation? Please explain.

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    $\begingroup$ Either the textbook or your quote is somewhat misleading. It is akin to saying that there are many solutions to the equation $x-5=0$, but only certain solution (that is, $x=5$) is "permissible" (that is, right). $\endgroup$ – Ivan Neretin Feb 2 '17 at 8:07
  • $\begingroup$ @IvanNeretin thanks for pointing out, I have corrected it. $\endgroup$ – jyoti proy Feb 2 '17 at 8:22
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    $\begingroup$ My comment still applies. Also, eigenvalues are surely not the solutions to the wave equation, either permissible or otherwise. $\endgroup$ – Ivan Neretin Feb 2 '17 at 8:24
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    $\begingroup$ Now it's OK. You have that E (energy) in the equation; it is just some number, but it can't be any number. There are certain permissible values for it, AKA eigenvalues. $\endgroup$ – Ivan Neretin Feb 2 '17 at 8:42
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    $\begingroup$ Mathematically there is nothing special about the Schrodinger equation as a differential equation. It is the boundary conditions we apply based on the physical situation, say length of box for particle in a box, that leads to quantised solutions, i.e. eigenvalues. $\endgroup$ – porphyrin Feb 2 '17 at 9:45

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