Jun 19, 2019 · The wave vector is perpendicular to the direction of motion of waves, by definition. Let's say you observe ...

Think about what the wave vector represents, and what kind of wave your equation describes. The most general equation for the spatial variation of the electric field for a plane wave is $$\mathbf{E}(\mathbf{r}) = \mathbf{E_{0}} e^{-i\mathbf{k} \bullet \mathbf{r}}$$ where $\mathbf{E_{0}}$ is some vector with no dependence on $\mathbf{r}$.

Oct 16, 2016 · $\begingroup$ I would like to point out that the concept of the wave vector in lattice vibrations (or vibrations in general) has nothing to do with Quantum theory, it is a purely classical concept. If you simply want to enumerate the eigenmodes of vibration for a lattice of harmonic springs, the wave vector picture is the natural one.

Mar 17, 2016 · The "vector wave equation" is actually just three uncoupled wave equations, so we might as well just talk about the wave equation $\nabla^2 \phi=\frac{1}{c^2} \ddot{\phi}$. For the bit of intuition, the number of dimensions is a bit superfluous, so just consider one dimension, giving: $\partial_x^2 \phi=\frac{1}{c^2} \partial_t^2\phi$.

The "direction of wave propagation" is the direction of a wave's energy flow, and the direction that a small wave packet will move, i.e. the direction of the group velocity. For light waves, this is also the direction of the Poynting vector. On the other hand, the wave vector points in …

Feb 26, 2016 · People tend to set $\hbar=1$ and use momentum and wave vector synonymously. In a solid-state environment -- the case you are interested in -- the quantum numbers turn out to be the band index (which is typically the same as the atomic quantum numbers) and a momentum or wave vector. This arises from Bloch's theorem.

Aug 26, 2020 · Jackson gives the standard argument that the elapsed phase of the wave is proportional to the number of wave-crests that have passed the observer, and thus it must be frame-independent. Also, interference effects are due to differences in the phase of waves.

May 11, 2017 · These coordinates arise from using reduced wave vector coordinates, as stated in Dove Introduction to Lattice Dynamics, page 23: It is common practice to define the wave vector as normalized by the first reciprocal lattice vector lying along the direction of the wave vector. This gives hat is called the reduced wave vector. For our one ...

The basic classical interpretation of this expression is that EM waves, or any wave described by a null 'wave-4-vector' like gravitational waves, travel at the speed of light.

Jun 25, 2019 · The question is, how would we define the direction of the wave or rather how would we define the unit vector of the complex wave vector (I am thinking of something like $\hat{k}$). Because in the case of a real wave vector, there is a physically conceivable concept of a norm and we, therefore, divide the vector by its norm to arrive at a unit ...