Molecular Spectroscopy and Transitions

Molecular spectroscopy is a subfield in which molecular behavior is studied by employing electromagnetic radiation. The radiation is used to induce transitions between molecular eigenstates. The process of absorbing or emitting radiation must take place in such a way that energy is conserved. Thus, the quantum of energy available in an absorbed or emitted 

Whereas the transition frequencies of a molecule in some region of the electromagnetic spectrum (e.g., visible, infrared) give information on eigenenergy differences, it is quantum mechanics that relates such differences to molecular features such as the stiffness of different chemical bonds and the molecular structure. Some detective work may be involved because each measured absorption or emission frequency needs to be associated with assigned to) the specific pair of states involved in the transition. The task of extracting molecular information from a spectrum usually starts with assigning frequencies. 

To say that by energy conservation a transition between molecular eigenstates may occur if the photon involved in the transition has exactly the same energy does not tell why or 

When time, t, is considered in a quantum mechanical problem, there is an associated operator, and like a position coordinate, the operator for time is multiplication by t. Also, like position coordinate operators that have conjugate momentum operators, the time operator has a conjugate. This means there is another operator whose commutator with t is ih, just as in the case of the commutator of the conjugate operators of position x and momentum p,.. To find the operator that is conjugate with time, an operator equation is employed. Using/to designate an arbitrary function and G to be the operator we wish to find. 

Dimensional analysis of this operator shows that it will produce an energy quantity (namely, J-s/s = J) on applying it to a wavefunction. This operator, which will be designated as from here on, plays an important role in the time evolution or time dependence of wavefunctions. 

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