“To start, we will consider a single particle moving in three space dimensions under the influence of a general central potential. Later we will specialize to the case of a Coulomb potential, and work out the spectrum of hydrogen. One other classic problem, the harmonic oscillator, will be treated at the end of this chapter.”

—  Steven Weinberg

Source: Lectures on Quantum Mechanics (2012, 2nd ed. 2015), Ch. 2: Particle States in a Central Potential

Adopted from Wikiquote. Last update Sept. 27, 2023. History

Help us to complete the source, original and additional information

Do you have more details about the quote "To start, we will consider a single particle moving in three space dimensions under the influence of a general central …" by Steven Weinberg?
Steven Weinberg photo
Steven Weinberg 46
American theoretical physicist 1933

Related quotes

James Jeans photo

“Minkowski… supposed that this fourth dimension of time was not detached from and independent of the three dimensions of space. He introduced a new four-dimensional space to which ordinary space contributed three dimensions, and time one; we may call it 'space-time'…. The succession of positions which a particle occupied in ordinary space at a succession of instants of time would be represented by a line in space-time; this he called the 'world-line' of the particle…. Newton's absolute space and absolute time fell out of science, and they carried much with them in their fall. First to go was the concept of simultaneity…. It now became necessary to find a way of treating gravitation which should not involve simultaneity. Einstein found through the medium of his 'Principle of Equivalence'.”

James Jeans (1877–1946) British mathematician and astronomer

The Growth of Physical Science (1947)

Jim Peebles photo

“A solid stores energy in the vibrations of the atoms about their equilibrium positions. In the simplest approximation, which Einstein considered, each atom vibrates with the same frequency, ν, in each of three dimensions, so a solid containing N atoms can be thought of as 3N one-dimensional simple harmonic oscillators.”

Jim Peebles (1935) Canadian-American astronomer

[Quantum Mechanics, 1992, Princeton University Press, 11, https://books.google.com/books?id=hTaw4Ht4Vi8C&pg=PA11]

Sidney Coleman photo

“The career of a young theoretical physicist consists of treating the harmonic oscillator in ever-increasing levels of abstraction.”

Sidney Coleman (1937–2007) American physicist

Said during one of his lectures at Harvard University http://www.physics.harvard.edu/about/Phys253.html.

“We are all such a waste of our potential, like three-way lamps using one-way bulbs.”

Mignon McLaughlin (1913–1983) American journalist

The Complete Neurotic's Notebook (1981), Unclassified

Maya Angelou photo

“One isn't necessarily born with courage, but one is born with potential. Without courage, we cannot practice any other virtue with consistency. We cannot be kind, true, merciful, generous, or honest.”

Maya Angelou (1928–2014) American author and poet
Václav Havel photo

“Classical modern science described only the surface of things, a single dimension of reality. And the more dogmatically science treated it as the only dimension, as the very essence of reality, the more misleading it became.”

Václav Havel (1936–2011) playwright, essayist, poet, dissident and 1st President of the Czech Republic

The Need for Transcendence in the Postmodern World (1994)
Context: Classical modern science described only the surface of things, a single dimension of reality. And the more dogmatically science treated it as the only dimension, as the very essence of reality, the more misleading it became. Today, for instance, we may know immeasurably more about the universe than our ancestors did, and yet, it increasingly seems they knew something more essential about it than we do, something that escapes us.

“Treating a being as an end in itself means respecting the value of what makes it such an end. After we see that this value resides in rational nature, we see it implies that, at least in general, rational beings should not be subjected to deception or coercion. Instead, we should seek to harmonize our strivings with those of other rational beings toward their ends.”

Allen W. Wood (1942) academic

Kantian Ethics (2008)

“For Linnaeus, Homo sapiens was both special and not special. […] Special and not special have come to mean nonbiological and biological, or nurture and nature. These later polarizations are nonsensical. Humans are animals and everything we do lies within our biological potential. […] [T]he statement that humans are animals does not imply that our specific patterns of behavior and social arrangements are in any way directly determined by our genes. Potentiality and determination are different concepts.”

Stephen Jay Gould book Ever Since Darwin

"Biological Potentiality vs. Biological Determinism", p. 251
Ever Since Darwin (1977)

Pierre Teilhard De Chardin photo

“To the cosmic corpuscles we should find it natural to attribute an individual radius of action as limited as their dimensions. We find, on the contrary, that each of them can only be defined by virtue of its influence on all around it. Whatever space we suppose it to be in, each cosmic element radiates in it and entirely fills it. However narrowly the heart of an atom may be circumscribed, its realm is co-extensive, at least potentially, with that of every other atom. This strange property we will come across again, even in the human molecule.”

Pierre Teilhard De Chardin book The Phenomenon of Man

The Phenomenon of Man (1955)

James Frey photo

“All of us started normal. All of us started out as functioning human beings with the potential to do almost anything we wanted, but somewhere along the paths of our lives, we got lost.”

James Frey book A Million Little Pieces

page 332
Source: A Million Little Pieces (2003)
Context: All of us started out normal. All of us started out as functioning human beings with the potential to do almost anything we wanted, but somewhere along the paths of our lives we got lost. Though we are here at this Clinic trying to find our way back, we all know that most of us will never get there. Things like the fight allow us to dream, and take us away from here, and allow us to imagine what the normal World must be like and how normal people must live in it.

Related topics