QM...just a few more digits?
Ivan Seeking:
"Thanks to QM, anyone alive today has a chance of living 400 - 600 years"...?
I like where you were going up until then...I think you are streching things a bit.
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About the uses of QM in engineering, I have a unique perspective to answer this question. I have an undergrad. physics degree and have recently joined an elect. engineering dept.
P.S. I love the list TOM gave, I want to elaborate on one or two of these who aren't familiar with the role QM plays in the device applications.
PET (positron emission tomography):
The PET scanner, used in medical imaging, fundamentally relies on the positron. It was theoretically predicted by Dirac when he devised a relativistically correct "Schroedinger Equation", called the Dirac equation. A natural consequence of the theory showed that particles resembling electrons, only with an opposite charge, must exist. It was decades later when Anderson experimentally observed the positron.
Lasers:
Quantum heterostructure devices, such as a MQW (multi-quantum-well) laser, fundamentally rely on the quantization of energy levels due to quantum confinement and the always fascinating phenomenon known as quantum tunneling.
Atomic physics:
Something as simple as looking at the discrete spectrum (the different colours of light) coming off of an arc-lamp (something similar to a fluorescent light), can't be explained without quantum mechanics.
So, you see, although one can look at QM and observe that it produces more accurate results for, say, the dynamics of macroscopic objects, the NEW, PREVIOUSLY-UNPREDICTED results is what makes it ground-breaking and (without exageration) revolutionary.
Another comment I have:
Semi-classical electrodynamics is OK depending on what you want the theory to do for you, and some may be satisfied with it, but it has limited scope. When people use semi-classical theories to explain phenomena, it is implied that quantum effects are insignificant or (remarkably) coincide with quantum results for DEEPER reasons. When this is the case, why use QM? For example, I don't use Schrodinger's equation to solve the trajectory of a baseball, do I (it would be much harder, if not impossible analytically)? I am pretty sure Prof. Jaynes would have agreed with me.
For example, atomic lifetimes:
The classical lifetime of an atomic excited state has a classical expression, but it is simply wrong. One can't do laser spectroscopy and predict lifetimes (or atomic linewidths) using a semi-classical theory.
Here is an example of when a classical approach is fine, Rutherford scattering:
Classical mechanics (and electrostatics) predict a certain differential scattering cross-section to be observed when alpha particles strike a thin metallic foil, and the results agree with observations. Why? The theory got lucky.
When one uses QM to solve the problem given the nuclear potential making the Born approximation (among others), calculating the scattering amplitude the same result is obtained. So why do the two agree, sheer luck (my intuition tells me there may be a deeper reason, but I don't know what it is).
In this case, however, the math involving both solutions are comparable in difficulty, so it is the physicists choice how he wants to model his results.
