Quantum physics
De Broglie’s proposal
Louis de Broglie proposed that all matter particles also exhibit wave-like behavior.
The photon, which is both a particle and a wave, is a clear example of this duality.
Particles possess both wave-like and particle-like attributes; particle attributes are
due to their specific amounts of energy and momentum, which are packaged into
discrete bundles. On the other hand, wave attributes include frequency and
amplitude. These are universal qualities of all particles, and collectively, they are
referred to as matter waves. Several experiments have been conducted over the
years to demonstrate the existence of matter waves. For example, recently,
scientists have been able to use particles - including molecules weighing up to
10,000 atomic mass units - to observe wave-like properties in action. In some
cases, electrons have been used in experiments that have resulted in striking
visuals, showing how they collide with screens placed in their path.
De Broglie wavelength in different frames:
One interesting fact about a free particle with momentum p is that it can be
associated with a plane wave with a wavelength of λ equaling Planck's
constant divided by p. This wave eventually becomes a well-known wave
function in Schrödinger's equation, which is a wave equation for these matter
waves. However, the nature of this number can be a little strange when we
consider special relativity. Imagine a particle moving with some momentum
and you associate this momentum with some wavelength, then you ask
another person moving relative to you, "how about this particle's
wavelength?". If one is moving relative to you, then the difference in
velocities is given by the subtraction of the velocity that the frame is moving.
So, if this particular particle has some high velocity with respect to the lab
frame, it will have a smaller velocity. This means that the de Broglie
wavelength associated with this particle will differ substantially from the
original value. Therefore, if you have a free particle with momentum p, it can
be associated with a plane wave with a wavelength of λ = h / p, which
becomes a wave function in Schrödinger's equation. However, this
De Broglie’s proposal
Louis de Broglie proposed that all matter particles also exhibit wave-like behavior.
The photon, which is both a particle and a wave, is a clear example of this duality.
Particles possess both wave-like and particle-like attributes; particle attributes are
due to their specific amounts of energy and momentum, which are packaged into
discrete bundles. On the other hand, wave attributes include frequency and
amplitude. These are universal qualities of all particles, and collectively, they are
referred to as matter waves. Several experiments have been conducted over the
years to demonstrate the existence of matter waves. For example, recently,
scientists have been able to use particles - including molecules weighing up to
10,000 atomic mass units - to observe wave-like properties in action. In some
cases, electrons have been used in experiments that have resulted in striking
visuals, showing how they collide with screens placed in their path.
De Broglie wavelength in different frames:
One interesting fact about a free particle with momentum p is that it can be
associated with a plane wave with a wavelength of λ equaling Planck's
constant divided by p. This wave eventually becomes a well-known wave
function in Schrödinger's equation, which is a wave equation for these matter
waves. However, the nature of this number can be a little strange when we
consider special relativity. Imagine a particle moving with some momentum
and you associate this momentum with some wavelength, then you ask
another person moving relative to you, "how about this particle's
wavelength?". If one is moving relative to you, then the difference in
velocities is given by the subtraction of the velocity that the frame is moving.
So, if this particular particle has some high velocity with respect to the lab
frame, it will have a smaller velocity. This means that the de Broglie
wavelength associated with this particle will differ substantially from the
original value. Therefore, if you have a free particle with momentum p, it can
be associated with a plane wave with a wavelength of λ = h / p, which
becomes a wave function in Schrödinger's equation. However, this
