Computational quantum chemistry is one. Researchers in pharmaceutics use computational quantum chemistry programs to model the interactions of small molecules (drugs or fragments of drugs) with proteins/DNA and predict whether or not the designed drug may or may not be effective for its purpose. They can do that before having to spend time and money synthesizing and testing dozens of drugs which may not have a chance to work at all.
A rather brief but nice explanation of how of computational quantum chemistry is applied in practice may be found in this website http://www.ccl.net/cca/documents/dyoung/topics-orig/contents.html.
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(I didn't expected this to become an accepted answer, just a contribution. Since having just one industrial application for computational quantum mechanics looks a bit sad, I'll add some others from what I know.)
The area I am working in is computational quantum chemistry so I know some more applications related to this. Computational quantum chemistry has become so widely used that developing software for it has become and industry by itself; examples are Schrodinger Inc. and Gaussian Inc. (just Google it). It is not only used in pharmaceutics, but also in the general chemistry industry. I know of big chemical companies that use similar simulations to the ones used in pharmaceutics, but for studying and developing catalysts rather than drugs.
Computational quantum mechanics methods for periodic systems are also widely used in material science. Density Funtional Theory methods are among the most popular. In the chemical industry, this is also used for the study and development of catalysts (catalysts can also be extended systems) as well as materials which can adsorb toxic or greenhouse gases such as CO or CO$_2$.
Closely related to computational quantum chemistry (or at least, the equations to solve and methods are similar) would be computational nuclear physics. I do not know to what extent do these methods are used in the nuclear energy industry, but I know the US Department of Energy funds this kind of research so I guess it must have some applications, although I am not qualified to develop more on this. On those lines, DoE also funds computational chemistry projects which can help develop alternative fuels.
Unfortunately, I am not aware of the kind of applications in electronics that you are interested in. However, I consider myself an ignorant in this area and it is quite possible that there may be a few applications out there.
