Of more formal properties of Eq. (84), it is easy to prove that its solutions satisfy the same continuity equation (1.52), with the probability current density \(\mathbf{j}\) still given by Eq. (1.47)...Of more formal properties of Eq. (84), it is easy to prove that its solutions satisfy the same continuity equation (1.52), with the probability current density \(\mathbf{j}\) still given by Eq. (1.47), but a different expression for the probability density \(w\) - which becomes very similar to that for \(\mathbf{j}\) : \[w=\frac{i \hbar}{2 m c^{2}}\left(\Psi^{*} \frac{\partial \Psi}{\partial t}-\text { c.c. }\right), \quad \mathbf{j}=\frac{i \hbar}{2 m}\left(\Psi \nabla \Psi^{*}-\text { c.c. }\…
One of the key points in particles physics is that special relativity plays a key rôle. As you all know, in ordinary quantum mechanics we ignore relativity. Of course people attempted to generate equa...One of the key points in particles physics is that special relativity plays a key rôle. As you all know, in ordinary quantum mechanics we ignore relativity. Of course people attempted to generate equations for relativistic theories soon after Schrödinger wrote down his equation. There are two such equations, one called the Klein-Gordon and the other one called the Dirac equation.
We have surreptitiously introduced the basic elements of non-relativistic quantum field theory. Consider again the Heisenberg model, where we described a lattice of spins with nearestneighbour interac...We have surreptitiously introduced the basic elements of non-relativistic quantum field theory. Consider again the Heisenberg model, where we described a lattice of spins with nearestneighbour interactions. If we take the limit of the lattice constant a→0 we end up with a continuum of creation and annihilation operators for each point in space. This is a field.
