![]() In an earlier lecture, we considered in some detail the allowed One Dimensional Infinite Depth Square Well This wave function is only relevant for positive x , and the coefficients A, B are functions of theĮnergy - for certain energies it turns out that A = 0 , and the wave function converges. Shall see below, there are situations with spatially varying potentials where Of course, this wave function will diverge in ![]() Ψ ( x ) tends to zero, the curvature tends to zero,įor a constant potential V 0 > E , the wave function is ψ ( x ) = A e α x + B e − α x, Will the curvature be just right to bring the wave function to zero as x goes to infinity. Only with exactly the right initial conditions Means that ψ ( x ) tends to diverge to infinity. Potential V ( x ) = V 0 E , the curvature is always away from the axis. The simplest example is that of a constant In bothĬases, ψ ( x ) is always curving towards the x -axis - so, for E > V ( x ), ψ ( x ) has a kind of stability: its curvature isĪlways bringing it back towards the axis, and so generating oscillations. This means that if E > V ( x ) , for ψ ( x ) positive ψ ( x ) is curving negatively, for ψ ( x ) negative ψ ( x ) is curving positively. ![]() Rate of change of slope, is the curvature – so the curvature of the function is Curvature of Wave Functionsĭ 2 ψ ( x ) d x 2 = 2 m ( V ( x ) − E ) ℏ 2 ψ ( x )Ĭan be interpreted by saying that the left-hand side, the Previous index next PDF Schrödinger’s Equation in 1-D: Some Examples ![]()
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