Question 2. Dirac equation.
Is the Dirac equation allegedly the generalised version of the advertised Schrödinger equation? If so, why is the Schrödinger equation still used everywhere by nuclear physics instead of the Dirac equation? Neoh.
Hi Neoh,
If you look at the Dirac equation as written for example on http://en.wikipedia.org/wiki/Dirac_equation it takes the same form as in the billboard. So the equation we have written captures both possibilities you mention if you specify the mathematical structure of Psi and H in the right way.
The Dirac equation is a modification of the Schrödinger equation made by Paul Dirac to accommodate “relativistic” situations – that is, when very high energies or speeds are involved. Now our theories for these instances have been developed further, so when such extremes are being encountered (which is not so common in nuclear physics) we would be using quantum field theory, which contains the Dirac equation implicitly built in.
The Dirac equation also only applies to one of the two particle types in nature – fermions and does not apply to the other vital type – bosons. (Bosons and fermions differ in the way they behave when put together: a light photon is an example of a boson – they act like teenagers, they want to behave the same and hang out together; an electron is an example of a fermion which is like a monk wanting to go off on their own.) Sometimes in nuclear physics we deal with bosons (many fermions clumped together can make a boson!) or we deal with fermions in situations where the fact there are other fermions around turn out to be unimportant – both of these allow us to use the Schrödinger equation instead of the Dirac equation (which is typically going to be more problematic to solve).
Terry
Is the Dirac equation allegedly the generalised version of the advertised Schrödinger equation? If so, why is the Schrödinger equation still used everywhere by nuclear physics instead of the Dirac equation? Neoh.
Hi Neoh,
If you look at the Dirac equation as written for example on http://en.wikipedia.org/wiki/Dirac_equation it takes the same form as in the billboard. So the equation we have written captures both possibilities you mention if you specify the mathematical structure of Psi and H in the right way.
The Dirac equation is a modification of the Schrödinger equation made by Paul Dirac to accommodate “relativistic” situations – that is, when very high energies or speeds are involved. Now our theories for these instances have been developed further, so when such extremes are being encountered (which is not so common in nuclear physics) we would be using quantum field theory, which contains the Dirac equation implicitly built in.
The Dirac equation also only applies to one of the two particle types in nature – fermions and does not apply to the other vital type – bosons. (Bosons and fermions differ in the way they behave when put together: a light photon is an example of a boson – they act like teenagers, they want to behave the same and hang out together; an electron is an example of a fermion which is like a monk wanting to go off on their own.) Sometimes in nuclear physics we deal with bosons (many fermions clumped together can make a boson!) or we deal with fermions in situations where the fact there are other fermions around turn out to be unimportant – both of these allow us to use the Schrödinger equation instead of the Dirac equation (which is typically going to be more problematic to solve).
Terry
