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A diabatic process is defined as follows:
Rapidly changing conditions prevent the system from adapting its configuration during the process, hence the spatial probability density remains unchanged. Typically there is no eigenstate of the final Hamiltonian with the same functional form as the initial state. The system ends in a linear combination of states that sum to reproduce the initial probability density.
An adiabatic process is defined as follows:
Gradually changing conditions allow the system to adapt its configuration, hence the probability density is modified by the process. If the system starts in an eigenstate of the initial Hamiltonian, it will end in the corresponding eigenstate of the final Hamiltonian.
A diabatic process involves a sudden change of the Hamiltonian, while an adiabatic process involves a gradual change of the Hamiltonian.
The word adiabatic, in thermodynamics, is usually reserved for processes that do not involve the exchange of heat between the system and surroundings. Does this use of the word adiabatic have any relation to the use of the word adiabatic in quantum mechanics? How about the word diabatic?