![]() ![]() Examples are provided in Chapter 4, Activity 2, and Chapter 5, Activity 1. ![]() In this situation, the oscillatory time dependence does not cancel out in calculations, but rather accounts for the time dependence of physical observables. For them to have the same slope we must have kA k1B. For them to have the same value, we see from above that A B. When a system is not is a stationary state, the wavefunction can be represented by a sum of eigenfunctions like those above. Schrdinger’s equation requires that the wavefunction have no discontinuities and no kinks (discontinuities in slope) so the x < 0 and x > 0 wavefunctions must match smoothly at the origin.A wavefunction with this oscillatory time dependence e-iωt therefore is called a stationary-state function. We will see that all observable properties of a molecule in an eigenstate are constant or independent of time because the calculation of the properties from the eigenfunction is not affected by the time dependence of the eigenfunction. deriving Interpretation Schrodingers equation Statistical In summary: This indeed is an important assumption of the Gleasons theorem, but there is an even more important one: The aditivity of the expectation values for commuting observables. ![]() When molecules are described by such an eigenfunction, they are said to be in an eigenstate of the time-independent Hamiltonian operator. ![]()
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