A shape of a surface illustrated in any such plot implies an associated formula, and vice versa; such a shape is meaningless in the absence of both such a formula and the specified system of coordinates, and even a specific constant value of that formula.
Unlike energy quantum number n that is independent of any system of coordinates and that arises indisputably from experiment, quantum numbers k and l have only a parochial significance: they are artifacts of this particular system and can be accordingly expected to have no meaning for the formulae and shapes of surfaces of amplitude functions apart from this system.
The X-axis of Ott's system of coordinates was set in accordance with the third sheet line of the East column XIX to the West (dc) and the Y-axis in accordance with the fourth sheet line of the 9th layer to the South (hi) of the stable cadastre system (Fig.
The coordinates of the origin of Ott's system of coordinates in the stable cadastre system are as follows:
The problem of nonlinear bending of a strip of polystyrene is analyzed using the orthogonal system of coordinates. This is another problem of analysis of physically nonlinear behaviour of polystyrene and one is to have in mind that though some quantities are denoted by the same letters as in the previous problem, they have a different meaning here.
Here physically nonlinear behaviour of a strip of polystyrene is analyzed using the model of a straight beam in the status of equilibrium coinciding with the x axis of the orthogonal system of coordinates. At both ends of a strip of polystyrene both generalized displacements are assumed equal to zero.
The output signals of coordinate changing unit U1 are the module of rotor magnetic field [[psi].sub.2m] and the projections of the current vector in the system of coordinates x, y used as feedback signals in the channels of magnetic field and torque control.
Following the expression of current and field vectors by the integral components and subsequently, identifying the real axis of the rotating system of coordinates with the rotor field vector, we obtain [[psi].sub.2x] = [[psi].sub.2m], [[psi].sub.2y] = 0.
shows no dependence on the angular variable, merely an exponential decay with distance from the origin of the system of coordinates that is effectively at the atomic nucleus, because [u.sup.2] + [v.sup.2] in the exponent is equivalent to distance 2 r from the nucleus.
Quantum numbers in each set n1, n2, m and each amplitude function that they designate, with their corresponding plots, are all parochial to this system of paraboloidal coordinates, just as quantum numbers k, l, m and their associated amplitude functions are parochial to the system of spherical polar coordinates, and have no meaning beyond the context of the same particular system of coordinates; equatorial quantum number fortuitously happens to be common to both systems because equatorial angle [phi] is likewise a common coordinate.
Finite-difference approximation of the Navier-Stokes and the flow continuity equations for this system of coordinates
contains the Coulomb force components [F.sub.x], [F.sub.y] and the flow velocity components [w.sub.x], [w.sub.y]:
As this system of coordinates
is routinely explained in most textbooks on quantum mechanics in physics and chemistry, we here present merely the most relevant aspects for comparison with solutions in other systems of coordinates.