Waves moving in a lecture

[Stefan Ram]

In the third lecture of the series "New Revolutions in
Particle Physics: Basic Concepts" (Fall, 2009) from "The
Theoretical Minimum", Professor Susskind talks about what
a quantum field is and how it is related to particles.

He considers a circle with a coordinate "x" and an amplitude
"exp( i k x )", and says that the momentum "p" is "hbar k".

Then he says (about 8 or 9 minutes into the video):

|"k" is called the "wave number". Uh. It's a wave number.
|And it can be positive or negative? Waves moving to the left,
|moving to the right, corresponding to momenta, going to the
|left or the right.

How can he talk about "waves moving to the left" if his
amplitude "exp( i k x )" does not depend on the time
(contains no "t")?

Do you think that "exp( i k x )" without "t" in his model
means that the amplitudes are constant (not depending on
the time) or is "exp( i k x )" a snapshot of the situation
taken at one instant (but actually depending on the time)?

[Richard Livingston]

I haven't seen this lecture, but if he is working in the
Heisenberg picture, the wave function is static and
all time dependence is in the operators. The effect
wrt your question is that there is an assumed
e^(-i \omega t) factor that appears when the position
operator is applied.

Rich L.