for that particular quantum number and the subscript is the quantum number. As an example of how the full orbital names are generated for real orbitals, one may calculate . From the table of spherical harmonics, with . Then Likewise . As a more complicated example: In all these cases we generate a Cartesian label for the orbital by examining, and abbreviating, the polynomial in , , and appearing in the numerator. We ignore any terms in the polynomial except for the term with the highest exponent in . We then use the abbreviated polynomial as a subscript label for the atomic state, using the same nomenclature as above to indicate the and quantum numbers. The expression above all use the Condon–Shortley phase convention which is favored by quantum physicists. Other conventions for the phase of the spherical harmonics exists. Under these different conventions the and orbitals may appear, for example, as the sum and difference of and , contrary to what is shown above. Below is a list of these Cartesian polynomial names for the atomic orbitals. Note that there does not seem to be reference in the literature as to how to abbreviate the long Cartesian spherical harmonic polynomials for so there does not seem be consensus on the naming of orbitals or higher according to this nomenclature. Shapes of orbitals Simple pictures showing orbital shapes are intended to describe the angular forms of regions in space where the electrons occupying the orbital are likely to be found. The diagrams cannot show the entire region where an electron can be found, since according to quantum mechanics there is a non-zero probability of finding the electron (almost) anywhere in space. Instead the diagrams are approximate representations of boundary or contour surfaces where the probability density has a constant value, chosen so that there is a certain probability (for example 90%) of finding the electron within the contour. Although as the square of an absolute value is everywhere non-negative, the sign of the wave function is often indicated in each subregion of the orbital picture. Sometimes the function is graphed to show its phases, rather than which shows probability density but has no phase (which is lost when taking absolute value, since is a complex number). orbital graphs tend to have less spherical, thinner lobes than graphs, but have the same number of lobes in the same places, and otherwise