principal quantum number

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Related to Radial quantum number: Principal quantum number

principal quantum number

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Two other intersections of the curve with those two lines occur, both near 1.07x[10.sup.-10] m; the latter location marks the presence of a nodal surface, the single spherical surface between r = 0 and r [right arrow] [infinity] at which function [[psi].sub.1,0,0] has zero amplitude and [[psi].sub.1,0,0.sup.2] = 0, consistent with radial quantum number k = 1.
Parameters that appear in the solution but not in the partial-differential equation take discrete values, imposed by boundary conditions, as follows: m is called the equatorial, or magnetic, quantum number that assumes only integer values and that arises in the solution of the angular equation to define [PHI]([phi]), as in spherical polar coordinates; the first arguments of the associated Laguerre functions, m and n2, like radial quantum number k among the three quantum numbers pertaining to spherical polar coordinates, must be non-negative integers so that for bound states of the hydrogen atom the Laguerre functions in U(u) and V(v) terminate at finite powers of variable u or v, and remain finite for u or v taking large values, respectively.
When d [right arrow] 0, [n.sub.[xi]] [right arrow] radial quantum number k for spherical polar coordinates, [n.sub.[eta]] [right arrow] l - [absolute value of m]; when d [right arrow] [infinity], [[eta].sub.xi]] [right arrow] paraboloidal quantum number n1 and [n.sub.[eta]] [right arrow] n2 [8].