Wave Equations, Wave Functions and Orbitals

Consider a standing wave in a stretched string. As we proceed horizontally along the string, the vertical displacement (or amplitude) of the wave increases in one direction, passes through a maximum, decreases to zero and then increases in the opposite direction. The places where the amplitude is zero are called nodes. The nodes lie on a plane called the nodal plane (which lies perpendicular to the plane of the paper along the x-axis in the above diagram). Upward displacement and downward displacement correspond to opposite phases of the wave. To distinguish between the two phases, one is given a ‘+’ sign and the other a ‘–‘ sign. If two waves are superimposed exactly out-of-phase (crests of one overlapping with the troughs of the other), they would cancel each other (sum of their amplitudes will become zero).