Posts Tagged ‘Schrödinger

On the origins of the Schrödinger equation

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Physicists have obtained the Schrödinger equation (shown here) from a mathematical identity. Their approach shows that the linearity of quantum mechanics is intimately connected to the strong coupling between the amplitude and phase of a quantum wave.

Physicists have obtained the Schrödinger equation (shown here) from a mathematical identity. Their approach shows that the linearity of quantum mechanics is intimately connected to the strong coupling between the amplitude and phase of a quantum wave.

One of the cornerstones of quantum physics is the Schrödinger equation, which describes what a system of quantum objects such as atoms and subatomic particles will do in the future based on its current state.

The classical analogies are Newton’s second law and Hamiltonian mechanics, which predict what a classical system will do in the future given its current configuration. Although the Schrödinger equation was published in 1926, the authors of a new study explain that the equation’s origins are still not fully appreciated by many physicists.

In a new paper published in PNAS, Wolfgang P. Schleich, et al., from institutions in Germany and the US, explain that physicists usually reach the Schrödinger equation using a mathematical recipe. In the new study, the scientists have shown that it’s possible to obtain the Schrödinger equation from a simple mathematical identity, and found that the mathematics involved may help answer some of the fundamental questions regarding this important equation.

Although much of the paper involves complex mathematical equations, the physicists describe the question of the Schrödinger equation’s origins in a poetic way: “The birth of the time-dependent Schrödinger equation was perhaps not unlike the birth of a river.

Often, it is difficult to locate uniquely its spring despite the fact that signs may officially mark its beginning.

Usually, many bubbling brooks and streams merge suddenly to form a mighty river. In the case of quantum mechanics, there are so many convincing experimental results that many of the major textbooks do not really motivate the subject [of the Schrödinger equation’s origins].

Instead, they often simply postulate the classical-to-quantum rules….The reason given is that ‘it works.'” Coauthor Marlan O.

Scully, a physics professor at Texas A&M University, explains how physicists may use the Schrödinger equation throughout their careers, but many still lack a deeper understanding of the equation.

“Many physicists, maybe even most physicists, do not even think about the origins of the Schrödinger equation in the same sense that Schrödinger did,” Scully told “We are often taught (see, for example, the classic book by Leonard Schiff, ‘Quantum Mechanics’) that energy is to be replaced by a time derivative and that momentum is to be replaced by a spatial derivative.

And if you put this into a Hamiltonian for the classical dynamics of particles, you get the Schrödinger equation.

It’s too bad that we don’t spend more time motivating and teaching a little bit of history to our students; but we don’t and, as a consequence, many students don’t know about the origins.”….

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Written by physicsgg

April 8, 2013 at 5:07 pm


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What is life? The physicist who sparked a revolution in biology

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Erwin Schrödinger introduced some of the most important concepts in biology, including the idea of a ‘code’ of life

Insights from biology and computing built upon Schrödinger's genius, changing our view of life forever. Photograph: Rick Sammon/AP

Insights from biology and computing built upon Schrödinger’s genius, changing our view of life forever. Photograph: Rick Sammon/AP

Matthew Cobb
Seventy years ago, on 5 February 1943, the Nobel prizewinning quantum physicist Erwin Schrödinger gave the first of three public lectures at Trinity College, Dublin. His topic was an unusual one for a physicist: “What is Life?” The following year the lectures were turned into a book of the same name.

One of Schrödinger’s key aims was to explain how living things apparently defy the second law of thermodynamics – according to which all order in the universe tends to break down. It was this that led my colleague Professor Brian Cox to use Schrödinger as the starting point of his BBC series Wonders of Life, leading to What is Life? shooting up the Amazon sales chart.

But Schrödinger’s book contains something far more important than his attempt to fuse physics and biology. In that lecture 70 years ago, he introduced some of the most important concepts in the history of biology, which continue to frame how we see life.

At a time when it was thought that proteins, not DNA, were the hereditary material, Schrödinger argued the genetic material had to have a non-repetitive molecular structure. He claimed that this structure flowed from the fact that the hereditary molecule must contain a “code-script” that determined “the entire pattern of the individual’s future development and of its functioning in the mature state”.

This was the first clear suggestion that genes contained some kind of “code”, although Schrödinger’s meaning was apparently not exactly the same as ours – he did not suggest there was a correspondence between each part of the “code-script” and precise biochemical reactions.

Historians and scientists have argued over the influence of Schrödinger’s lectures and the book that followed, but there can be no doubt that some of the key figures of 20th century science – James Watson, Francis Crick, Maurice Wilkins and others – were inspired to turn to biology by the general thrust of Schrödinger’s work.

The role of the brilliant “code-script” insight is less clear. Reviewers of What is Life? in both Nature and the New York Times noted the novel phrase, but despite the fact that in 1944 Oswald Avery published clear evidence that DNA was the genetic material, virtually no one immediately began looking for – or even talking about – a molecular “code-script” in DNA, although Kurt Stern suggested that the code might involve grooves in a protein molecule, like the grooves in a vinyl disc.

Part of the reason for this lack of immediate excitement and for Avery’s discovery not being widely accepted was that DNA was thought to be a “boring” molecule with a repetitive structure – exactly what Schrödinger had said a gene could not be. It took the work of Erwin Chargaff, inspired by Avery, to show that the proportion of the “bases” in the DNA molecule – generally presented by the letters A, T, C and G – differed widely from species to species, suggesting the molecule might not be so boring after all.

As early as 1947, Chargaff suggested that the change of a single base “could produce far-reaching changes … it is not impossible that rearrangements of this type are among the causes of the occurrence of mutations.” The culmination of this line of work was Watson and Crick’s double helix model, which was based on the experimental data of Rosalind Franklin and Maurice Wilkins.

But in 1947 there was a missing component in biological thinking about the nature of the code, one which was at the heart of Watson and Crick’s decisive interpretation of their discovery a mere six years later – “information”. That idea entered biology through some applied research carried out to aid the war effort.

In 1943, the US National Research and Development Committee set up a group of scientists to study “fire control” – how to ensure accurate anti-aircraft fire, by the control of information from radar, visual tracking and range-finding. Two of the men involved in this project were Claude Shannon, a mathematician who developed what became known as “information theory” to understand how signals were processed, and Norbert Wiener, who thought there were parallels between control systems in machines and in organisms, and who coined the term “cybernetics”.

The first person to argue that a gene contains information was the co-founder of cybernetics, John von Neumann. In 1948, von Neumann described a gene as a “tape” that could program the organism – like the “universal Turing machine” described in 1936 by Alan Turing (intriguingly, Turing had discussed it with Shannon while working in New York in 1944). A few years later in 1950, geneticist Hans Kalmus deliberately applied cybernetic thinking to the problem of heredity and suggested that a gene was a “message”.

Cybernetics briefly became wildly popular, filling the pages of broadsheet newspapers all over the world and encouraging biologists to look for feedback loops in living things. Following the 1948 publication of Shannon’s dense book Information Theory (co-authored by Warren Weaver, who had chaired the fire control group and also coined the term “molecular biology”), the abstract concept of information percolated into the scientific mainstream.

Although the term had a precise meaning for Shannon, in the hands of the biologists it turned into a vague metaphor, a way of thinking about something they as yet had no real understanding of: the nature of the gene.

Ten years after Schrödinger’s brilliant insight, Watson and Crick’s second 1953 article on the structure of DNA provided the world with the key to the secret of life, casually employing the new concepts that had been created by cybernetics and propelling biology into the modern age with the words: “it therefore seems likely that the precise sequence of the bases is the code which carries the genetical information.”

These prophetic words – shorn of the conditional opening phrase – are uttered in biology classes all over the world, every single day.

In a decade of tumultuous discovery, insights from biology and computing built upon Schrödinger’s genius, changing our view of life forever. Life had become information, genes were the bearers of that information, carrying it in a tiny, complex code inside every cell of our bodies. And the breakthrough began in a Dublin lecture theatre 70 years ago this week.
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Written by physicsgg

February 7, 2013 at 4:56 pm

Posted in BIOLOGY

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How Einstein Discovered Dark Energy

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Alex Harvey
In 1917 Einstein published his Cosmological Considerations Concerning the General Theory of Relativity. In it was the first use of the cosmological constant. Shortly thereafter Schröodinger presented a note providing a solution to these same equations with the cosmological constant term transposed to the right hand side thus making it part of the stress-energy tensor. Einstein commented that if Schröodinger had something more than a mere mathematical convenience in mind he should describe its properties. Then Einstein detailed what some of these properties might be. In so doing, he gave the first description of Dark Energy. We present a translation of Schrödinger’s paper and Einstein’s response….
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Read also: The Cosmological Constant

Written by physicsgg

December 1, 2012 at 6:21 pm


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5 Of Physics’s Greatest Sex Scandals

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Physicists need love, too. Just ask Paul Frampton, the physics professor who was sentenced recently after an alleged scam involving drugs and a bikini model.
We know it can be hard to resist the temptation of bikini models on the Internet, but physicist Paul Frampton was duped pretty bad. The University of North Carolina professor flew to Bolivia to meet up with model Denise Milani, but Milani never showed up. Instead, a man with a briefcase claiming to be Milani’s intermediary sent Frampton on a drug smuggling mission. Frampton was arrested before he made it back the United States and convicted last week. We’re all fools in love, huh?

Frampton isn’t the only physicist to get caught up in a love scandal. Though most of them haven’t ended up in an Argentine prison, some did have awkward run-ins with the media. Check out these physicists who probably wish their sex lives were as invisible as dark matter.

Albert Einstein’s theory of relatives
The father of relativity wasn’t very good to his second first wife, Mileva Maric. He made her do all the housework, and in return, she got… well, nothing much in the love department. That’s because he was too busy taking lovers, including his cousin Elsa whom he later married. When asked about his love life, he would probably say, “It’s all relatives.” Zing!

Marie Curie’s radioactive love
Apparently, two Nobel prizes aren’t enough to get people off your back about that one affair you had. After Marie Curie’s husband died, she fell in love with his former student, Pierre Langevin. The man was married, so the French press made a big stink about it and started calling her a homewrecker and a Jew. For the record, Curie was not cheating on anyone herself (and was also not Jewish.)

Erwin Schrodinger’s mistresses
Here we have another physicist who wanted little do with his wife. Austrian physicist Erwin Schrodinger had several mistresses, one being the wife of his assistant, Arthur March. The weird part: March was cool with it and stepped in as the father of the child while his wife Hilde moved into the Schrodinger household.

Stephen Hawking and the sex clubs
It doesn’t really seem fair to pick on Hawking for a few reasons, the main one being that he currently doesn’t have a wife to cheat on, but the media did it anyway. Hawking apparently frequents the sex clubs, and the only reason that’s a scandal is because it is now horrendously public. No one’s getting hurt here, at the very least.
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Written by physicsgg

November 28, 2012 at 1:50 pm

Isaac Newton and Erwin Schrödinger

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Today is Schrodinger‘s birthday (12 August 1887 – 4 January 1961)

Written by physicsgg

August 12, 2012 at 4:14 pm

Posted in HUMOR

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Rotating Schrödinger’s Cat To Death

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You may suspect the beating of a dead horse by now, but the problem is actually that the animals in question are still alive. As was discussed, the alive cats expect to see something when the box opens.
If we interact with the Schrödinger cat superposition state inside the otherwise isolated box so that we will only have dead cats result, what do the alive cats see? There must be a place into which those cats can jump. However, it cannot be the room where the experimenter observes them, since the experimenter only observes dead cats after having applied the ‘rotation’.
Judging from the comments, this question is harder than anticipated, so before merely giving the solution, let us clarify the problem further. It is worth it, because the answer is quite simple and not at all philosophically nebulous, though certainly philosophically relevant…………… Read more:

Written by physicsgg

May 13, 2011 at 2:35 pm


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If Schrödinger Cats All Die, Do The Alive Ones Go To Hell?

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Schrödinger’s cat is in a quantum superposition of two states, namely |Dead> and |Alive>. If we open the box and find the cat dead, where is the living one? You all know the answer: In the ‘parallel universe’ where I pull the cat out alive. Let me add a twist that only a true cat hater can come up with…..Read more:

Written by physicsgg

May 3, 2011 at 9:40 pm

Schrödinger’s cat and quantum computers

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Written by physicsgg

April 30, 2011 at 5:19 pm