The constraints on n, \(l\) \(l)\), and \(m_l\) that are imposed during the solution of the hydrogen atom Schrödinger equation explain why there is a single 1s orbital, why there are three 2p orbitals, five 3d orbitals, etc. The wavefunction with n = 1, \(l\) \(l\) = 0 is called the 1s orbital, and an electron that is described by this function is said to be “in” the ls orbital, i.e. So, equation (2) and the more conventional equation from Griffith are equations for different functions. II Schroedinger’s equation in spherical polar coordinates The magnitude of a central force on an object depends on only the distance of that object from the origin the direction of the force is along the line joining the origin and the object. The location of the angular nodal surfaces is determined by the contributing angular momentum states. An atomic orbital is a function that describes one electron in an atom. The difference is due to the fact that solid harmonics are not spherical harmonic. Details of the derivation of the formulae appear elsewhere 11. The approximate state designation for the log SE with a central potential is determined by the dominant angular momentum component in the summation additional contributing states are given in the third column. The hydrogen atom wavefunctions, \(\psi (r, \theta, \phi )\), are called atomic orbitals.
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