Uploaded January 2022 | Updated September 2026, 2 weeks ago
This slow video demonstrates something quite interesting imo.
Shown is a Gaussian wave packet, an electron, say, evolving according to the Schrödinger equation in a spiral shaped waveguide. When the wave packet enters the narrow channel transverse modes, transverse in the direction of propagation, are formed. The less number of transverse modes, the faster the speed of that part of the wave packet is, and vice versa. Since the number of allowed transverse modes must be an integer, the wave packet is tied up in discrete lumps in the channel, i.e. “quantized”.
The origin is that the total momentum, p = px + py, is conserved, and thereby that a portion of the wave having few transverse modes, thus has a relatively small transverse momentum which implies that the remaining momentum is left for forward motion. Consequently, portions of the wave being associated with a larger number of transverse modes moves slower in the spiral.
First part = probability density, second part = wave function (real part)
Music by @gpcbass - a beautiful song called Vanessa, youtube.com/watch?v=yE8G0kmfzjc, used many times on this channel.
This slow video demonstrates something quite interesting imo.
Shown is a Gaussian wave packet, an electron, say, evolving according to the Schrödinger equation in a spiral shaped waveguide. When the wave packet enters the narrow channel transverse modes, transverse in the direction of propagation, are formed. The less number of transverse modes, the faster the speed of that part of the wave packet is, and vice versa. Since the number of allowed transverse modes must be an integer, the wave packet is tied up in discrete lumps in the channel, i.e. “quantized”.
The origin is that the total momentum, p = px + py, is conserved, and thereby that a portion of the wave having few transverse modes, thus has a relatively small transverse momentum which implies that the remaining momentum is left for forward motion. Consequently, portions of the wave being associated with a larger number of transverse modes moves slower in the spiral.
First part = probability density, second part = wave function (real part)
Music by @gpcbass - a beautiful song called Vanessa, youtube.com/watch?v=yE8G0kmfzjc, used many times on this channel.
