Lets start with first quantization and the quantum mechanical wave function of a photon, before we start on wave packets, which belong to second quantisation.

The quantum mechanical equation for photons is a quantized Maxwell's equation,in various forms, an example  seen here

The $Ψ^*Ψ$ of this wavefunction is the probability of a photon to manifest at (x,y,z,t).

Note that the E and B fields are the ones that will appear in the classical beam made up of zillion of such photons by superposition of their wavefunctions. As complex numbers phases will appear which will carry the possibility of constructive and/or destructive interference patterns.

Now we come to wavepackets and second quantization. Second quantization uses the plane wave solutions of the photon wavefunction as the field on which creation and annihilation operators will operate to describe a real photon in (x,y,z,t). A single plane wave is not localized and one has to use the wavepacket mathematics to describe real photons, with adjacent frequencies in the field functions. These obey a form of the heisenberg uncertainty .

The way the superposition of photons generates the classical electromagnetic waves in quantum field theory can be seen in this blog post by Motl.

The interference patterns have been addressed in the other answers.

Lets start with first quantization and the quantum mechanical wave function of a photon, before we start on wave packets, which belong to second quantization.

The quantum mechanical equation for photons is a quantized Maxwell's equation, in various forms, an example as from $\operatorname{Eq.}{\left(11\right)}$ in this paper:

Now write the complex wave function as a sum of real and imaginary parts ${\vec{E}}_T \left( \vec{r} \right)$ and ${\vec{B}}_T \left( \vec{r} \right) ,$ $$ {\vec{\varPsi}}_T \left(\vec{r},t\right)={2}^{-1/2}\left(\vec{E}_T\left(\vec{r},t\right)+i \vec{B}_T\left(\vec{r},t\right)\right). \tag{11} $$

The $Ψ^*Ψ$ of this wavefunction is the probability of a photon to manifest at $\left(x,y,z,t\right).$

Note that the $\vec{E}$ and $\vec{B}$ fields are the ones that will appear in the classical beam made up of zillion of such photons by superposition of their wavefunctions. As complex numbers phases will appear which will carry the possibility of constructive and/or destructive interference patterns.

Now we come to wavepackets and second quantization. Second quantization uses the plane wave solutions of the photon wavefunction as the field on which creation and annihilation operators will operate to describe a real photon in $\left(x,y,z,t\right).$ A single plane wave is not localized and one has to use the wavepacket mathematics to describe real photons, with adjacent frequencies in the field functions. These obey a form of the Heisenberg uncertainty .

The way the superposition of photons generates the classical electromagnetic waves in quantum field theory can be seen in this blog post by Motl.

The interference patterns have been addressed in the other answers.

Lets start with first quantization and the quantum mechanical wave function of a photon, before we start on wave packets, which belong to second quantisation.

The quantum mechanical equation for photons is a quantized Maxwell's equation,in variou forms, an example seen here

The $Ψ^*Ψ$ of this wavefunction is the probability of a photon to manifest at (x,y,z,t).

Note that the E and B fields are the ones that will appear in the classical beam made up of zillion of such photons by superpostion of their wavefunctions. As complex numbers phases will appear which will carry the possibility of constructive and/or destructive interference patterns.

Now we come to wavepackets and second quantization. Second quantization uses the plane wave solutions of the photon wavefunction as the field on which creation and annihilation operators will operate to describe a real photon in (x,y,z,t). A single plane wave is not localized and one has to use the wavepacket mathematics to describe real photons, with adjacent frequencies in the field functions. These obey a form of the heisenberg uncertainty .

The way the superposition of photons generates the classical electromagnetic waves in quantum field theory can be seen in this blog post by Motl.

The interference patterns have been addressed in the other answers.

Lets start with first quantization and the quantum mechanical wave function of a photon, before we start on wave packets, which belong to second quantisation.

The quantum mechanical equation for photons is a quantized Maxwell's equation,in various forms, an example seen here

The $Ψ^*Ψ$ of this wavefunction is the probability of a photon to manifest at (x,y,z,t).

Note that the E and B fields are the ones that will appear in the classical beam made up of zillion of such photons by superposition of their wavefunctions. As complex numbers phases will appear which will carry the possibility of constructive and/or destructive interference patterns.

Now we come to wavepackets and second quantization. Second quantization uses the plane wave solutions of the photon wavefunction as the field on which creation and annihilation operators will operate to describe a real photon in (x,y,z,t). A single plane wave is not localized and one has to use the wavepacket mathematics to describe real photons, with adjacent frequencies in the field functions. These obey a form of the heisenberg uncertainty .

The way the superposition of photons generates the classical electromagnetic waves in quantum field theory can be seen in this blog post by Motl.

The interference patterns have been addressed in the other answers.