Quantum mechanics is the study of very small things. It explains the behavior of matter and its interactions with energy on the scale of atomic and subatomic particles. By contrast, classical physics explains matter and energy only on a scale familiar to human experience, including the behavior of astronomical bodies such as the Moon. Classical physics is still used in much of modern science and technology. However, towards the end of the 19th century, scientists discovered phenomena in both the large (macro) and the small (micro) worlds that classical physics could not explain. The desire to resolve inconsistencies between observed phenomena and classical theory led to two major revolutions in physics that created a shift in the original scientific paradigm: the theory of relativity and the development of quantum mechanics. This article describes how physicists discovered the limitations of classical physics and developed the main concepts of the quantum theory that replaced it in the early decades of the 20th century. It describes these concepts in roughly the order in which they were first discovered. For a more complete history of the subject, see History of quantum mechanics.
Light behaves in some aspects like particles and in other aspects like waves. Matter—the "stuff" of the universe consisting of particles such as electrons and atoms—exhibits wavelike behavior too. Some light sources, such as neon lights, give off only certain specific frequencies of light, a small set of distinct pure colors determined by neon's atomic structure. Quantum mechanics shows that light, along with all other forms of electromagnetic radiation, comes in discrete units, called photons, and predicts its spectral energies (corresponding to pure colors), and the intensities of its light beams. A single photon is a quantum, or smallest observable particle, of the electromagnetic field. A partial photon is never experimentally observed. More broadly, quantum mechanics shows that many properties of objects, such as position, speed, and angular momentum, that appeared continuous in the zoomed-out view of classical mechanics, turn out to be (in the very tiny, zoomed-in scale of quantum mechanics) quantized. Such properties of elementary particles are required to take on one of a set of small, discrete allowable values, and since the gap between these values is also small, the discontinuities are only apparent at very tiny (atomic) scales.
Many aspects of quantum mechanics are counterintuitive and can seem paradoxical because they describe behavior quite different from that seen at larger scales. In the words of quantum physicist Richard Feynman, quantum mechanics deals with "nature as She is—absurd".For example, the uncertainty principle of quantum mechanics means that the more closely one pins down one measurement (such as the position of a particle), the less accurate another complementary measurement pertaining to the same particle (such as its speed) must become.
Another example is entanglement, in which a measurement of any two-valued state of a particle (such as light polarized up or down) made on either of two "entangled" particles that are very far apart causes a subsequent measurement on the other particle to always be the other of the two values (such as polarized in the opposite direction).
A final example is superfluidity, in which a container of liquid helium, cooled down to near absolute zero in temperature spontaneously flows (slowly) up and over the opening of its container, against the force of gravity.
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I am reading Leonard Susskind's Theoretical Minimum book on Quantum Mechanics. Excercise 7.4 is as follows:
Calculate the density matrix for ##|\Psi\rangle = \alpha|u\rangle + \beta|d\rangle##.
Answer:
$$ \psi(u) = \alpha, \quad \psi^*(u) = \alpha^* \\
\psi(d) = \beta, \quad \psi^*(d) =...
If you have two similar coherent sources which are separated from each other by a barrier. Now one source sends particles one by one into one slit and the other sends particles into the other in a double slit interference experiment.
Now, the photons are always undistinguishable, so they should...
I am trying to solve for the uncertainty in energy ##\Delta E## in the following exercise:
$$\Delta E = \sqrt{\langle \Phi | (\hat H - \bar E )^2 | \Phi \rangle}$$
Questions
What does ##(\hat H - \bar E )^2## mean? Is it a simple binomial expansion into ##\hat H^2 - 2 \bar E \hat H + \bar...
In my introduction to quantum mechanics, I learned about the particle in a box, followed by the quantum harmonic oscillator. In both instances, zero energy was not possible; the ground states had non-zero energy.
However, in deriving the solutions to the Schrödinger equation for a particle on a...
If the universe was in an energy eigenstate then d<A>/dt = 0 for any dynamic variable A. Stuff moves which implies that the Universe isn't in an eigenstate. What factors drive the energy spread?
I have been trying to understand the role of a cavity as a black body radiator in the derivation of planks black body radiation law but it has left me with 5 main questions:
1. If an object is a perfect absorber it must also be a perfect emitter, meaning that (allowing for a cavity not being a...
Dear physics forums,
What is the physical interpretation of imposing the following constrain on a Hamiltonian:
Tr(\hat H^2)=2\omega ^2
where \omega is a given constant. I am not very familiar with why is the trace of the hamiltonian there.
Thanks in advance,
Alex