The role of quantum mechanics was originally to describe the behavior of individual atoms and molecules. This is the way of the Schrodinger equation or matrix mechanics, the harmonic oscillator, the hydrogen atom, infinite-dimensional Hilbert spaces, quantization, and so on. I would like to call it "hermitian" quantum mechanics since the Hamiltonian is a hermitian operator.
Then there is the quantum mechanics which describes engineered quantum systems like quantum dots and quantum logic gates. Here time evolution is in discrete steps, Hilbert spaces are finite-dimensional, and probabilities are discrete instead of continuous. I think it is apt to call this "unitary" quantum mechanics since one essentially only considers exponentiated Hamiltonians.
It is important not to confuse the two. If you know hermitian quantum mechanics then unitary quantum mechanics is conceptually straightforward. If you know unitary quantum mechanics then you will have a lot of new concepts and mathematics to learn before you understand hermitian quantum mechanics (but of course you may know more about applications).
The programs mentioned in the article teach unitary quantum mechanics: sufficient for engineering, insufficient for physics. If we assume that the engineering world is becoming increasingly quantum then it is perhaps not a bad thing.
There is radioactivity which was (and still) one of the most important aspects in physics (nuclear physics) and it is mainly about describing decaying state. This is using non-hermitian QM. Because of hermitian operators giving always real eigenvalues (This exercise is left to the reader) we can see (and prove) that non hermitian operators will give rise to complex eigenvalues whose imaginary eigenvalues mean that the probability of finding the particle decreases exponentially with time (decay).
That is actually an approximation that will violate the QM postulate that evolution shouls be unitary (and probability is not conserved obviously).
People who study that in a more rigorous way will go and define somehow bigger Hilbert space that not only include the particle (atom) but will also include the decay products and only when you solve the system with the states of mother plus daughters you will return to your ordinary simple/ish quantum mechanics.
The idea is that the decrease of probability of finding the particle will be opposed by increasing probability of finding decay products. So the total probability will be conserved and we will have unitary time operator.
Hint: It is not simple as ordinary QM when you sometimes have to worry about resonances, mixed states and modeling these things mathematically is much difficult that solving your ordinary hermitian hamiltonian.
Then there is the quantum mechanics which describes engineered quantum systems like quantum dots and quantum logic gates. Here time evolution is in discrete steps, Hilbert spaces are finite-dimensional, and probabilities are discrete instead of continuous. I think it is apt to call this "unitary" quantum mechanics since one essentially only considers exponentiated Hamiltonians.
It is important not to confuse the two. If you know hermitian quantum mechanics then unitary quantum mechanics is conceptually straightforward. If you know unitary quantum mechanics then you will have a lot of new concepts and mathematics to learn before you understand hermitian quantum mechanics (but of course you may know more about applications).
The programs mentioned in the article teach unitary quantum mechanics: sufficient for engineering, insufficient for physics. If we assume that the engineering world is becoming increasingly quantum then it is perhaps not a bad thing.