Schrfidinger equation

Xb discuss the problem of the interaction of light with an atomic or molecular system, it is essential to consider those perturbations which are functions of time. It is such perturbations that provoke transitions from one state to another in a given system. Thus, specifically, it is the time-dependbnt Schrfidinger equation that must be considered. It can be written in the form... 

The total wave function for one dimensional Schrfidinger equation for the nth energy state is written as,... 

Aside from relativistic and quantum electrodynamic effects, a single molecule in free space is completely described by the Schrfidinger equation (8-2.1)... 

The Schrfidinger equation multiplied by exp(-F) from the left becomes ... 

The resulting Schrfidinger equation may be solved by a perturbation treatment. As zeroth order basis functions we use products of rotational j, vibrational [ft)tin(E)], and electronic. ..)] wave functions. 

An exact solution to the Schrfidinger equation is not possible for any but the most trivial molecular systems. However, a number of simplifying assumptions and procedures do make an approximate solution possible for a large, inge of ii il.-i ule., . 

Xjv) in which each electron i is designated by the space, spin coordinates x,. In the non-relativistic Schrfidinger equation... 

The (0) equation, an angular part of the Schrfidinger equation describing the hydrogen atom, can be expressed as... 

For an electron in a central field, the Schrfidinger equation may be written as... 

One of die most important second-order, homogeneous differential equations is that of Hennite It arises in the quantum mechanical treatment of the harmonic oscillator. Schrfidinger s equation for the harmonic oscillator leads to the differential equation... 

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