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Qmechanic ♦
Qmechanic ♦
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Thomas Fritsch
Thomas Fritsch
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While solving SchrodingerSchrödinger equation for Hydrogen atom we make a scale transformation for radial variable (r=ax/Z;where a=Bohr$r=\frac{ax}{Z}$; where $a=$ Bohr radius, x=dimensionless$x=$ dimensionless variable and Z=atomic$Z=$ atomic number), this turns out to be a very good scale transformation. But my question is how do we know value of Bohr radius in advance, before solving schrodingerSchrödinger equation?Do Do we just use Bohr radius that we got from Bohr theory? If we do use Bohr radius from Bohr theory then why is so because it is a classical theory?

While solving Schrodinger equation for Hydrogen atom we make a scale transformation for radial variable (r=ax/Z;where a=Bohr radius, x=dimensionless variable and Z=atomic number), this turns out to be a very good scale transformation. But my question is how do we know value of Bohr radius in advance, before solving schrodinger equation?Do we just use Bohr radius that we got from Bohr theory? If we do use Bohr radius from Bohr theory then why is so because it is a classical theory?

While solving Schrödinger equation for Hydrogen atom we make a scale transformation for radial variable ($r=\frac{ax}{Z}$; where $a=$ Bohr radius, $x=$ dimensionless variable and $Z=$ atomic number), this turns out to be a very good scale transformation. But my question is how do we know value of Bohr radius in advance, before solving Schrödinger equation? Do we just use Bohr radius that we got from Bohr theory? If we do use Bohr radius from Bohr theory then why is so because it is a classical theory?

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Barry
Barry
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Hydrogen atom and scale transformation for radial variable

While solving Schrodinger equation for Hydrogen atom we make a scale transformation for radial variable (r=ax/Z;where a=Bohr radius, x=dimensionless variable and Z=atomic number), this turns out to be a very good scale transformation. But my question is how do we know value of Bohr radius in advance, before solving schrodinger equation?Do we just use Bohr radius that we got from Bohr theory? If we do use Bohr radius from Bohr theory then why is so because it is a classical theory?