# Schrodinger and His Equation — David Clary / Serious Science

In November the 9th 1933 the great Austrian

physicist Erwin Schrödinger came to this room, this office where I work, the office

of the president of Magdalen College. Schrödinger had been in a Solvay Conference

in Brussels; he came here and was admitted on that day as a fellow of Magdalen College

using Latin phrases that we use to the present day. After the ceremony in this room the phone

rang and it was from The Times of London. The Times of London said that Schrödinger

had just been awarded the Nobel Prize. So he was heard he’d won the Nobel Prize in

this room and the next day in The Times and The Telegraph newspapers it stated that Schrödinger

of Oxford University had won the Nobel Prize even though he’d actually been employed before

at the University of Berlin. What did Schrödinger win the Nobel Prize

for? Well, it was for a paper he wrote in 1926

when he introduced his famous Schrödinger equation. Up to that time the theory for explaining

the energy of electrons in atoms had really been due to the famous physicist Niels Bohr

who’d come up with a theory for explaining the spectrum of the hydrogen atom, the electronic

spectrum of the hydrogen atom, and fitting the energy levels with his own formula. But Bohr’s theory didn’t work very well at

all for other atoms or even for molecules: it didn’t seem to be a general one. What Schrödinger did is he came up with a

general equation that worked for the hydrogen atom and worked for predicting not just the

energy levels of the hydrogen atom but also the intensities of the spectral lines: whether

the lines in the spectrum are intense or not, he could predict that intensity. That was new. Not even his collaborators or the people who

were competing with him, like Heisenberg, knew how to do that and Schrödinger did it

with his equation. Then Schrödinger in the same year realized

that he could apply his equation not just to the electronic energy levels of the hydrogen

atom but to other problems, like the vibration of a harmonic oscillator, like to the rotation

of a diatomic molecule: the same equation could be applied and gave the results that

agreed with experiment for those sorts of problems. And then Schrödinger realized his equation

could also be adapted not just for simple processes, but for processes that depend on

time. In fact, there are two Schrödinger’s equations:

what’s called ‘the time independent equation’ and ‘the time dependent equation’. But why the equation became so significant

is that suddenly many scientists around the world realized that not only did it work for

the hydrogen atom: it worked for all atoms and all molecules in principle. That means it had remarkable applications

to nearly everything you can see, depends on atoms and molecules, and Schrödinger’s

equation can be used to calculate all their properties. If you solve this equation very accurately,

you get essentially the right answer. So it was a very powerful theory that came

out of Schrödinger’s great work in 1926 for all atoms and molecules. The problem is that his equation was quite

complicated mathematically and very difficult to solve for anything more complicated than

the hydrogen atom. Even for the helium atom it involved quite

a lot of difficult integration and differentiation and so on. So it didn’t really change science so much

in the very early days. But where the big change came with Schrödinger’s

equation was when computers came along: it was then possible to use computers to solve

his equation and do that really accurately as time has gone on more and more. That means Schrödinger’s equation can be

applied to more and more complicated systems and atoms, now to even to solid materials

and also to problems of biological importance: you can do calculations with Schrödinger’s

equation, for example, on proteins, on enzymes, on DNA and so on. So it’s become in the modern world an extremely

powerful theory: it’s the theory that underlies the whole of chemistry, molecular biology. In material science, understanding the properties

of materials, you can do calculations with Schrödinger’s equation and many people do

that. Even in geology you can calculate the temperature

the center of the Earth using variants of Schrödinger’s equation. So in the 21st century, it’s become almost

the essential tool for doing simulations on atoms and molecules. The other method before Schrödinger was developed

by Isaac Newton: Newton’s laws. You could simulate atoms and molecules using

Newton’s laws but those don’t include crucially quantum mechanical effects, such as tunneling,

such as probability: these laws just don’t work for atoms and molecules, but Schrödinger’s

equation does. So Schrödinger came here in 1933 and he came

to work here in Oxford: he was a fellow in my college, he lectured at the University

of Oxford on the quantum theory. But he wasn’t very happy here. He had an appointment which was almost like

a postdoctoral assistant: after being a top professor in the University of Berlin he had

an appointment that was just renewed every year, funded by ICI, the chemical company. So he wasn’t very happy. He was here just for three years and he missed

his great friends in Berlin: he was he was very friendly with Max Planck, the person

who discovered quantum theory. He was very friendly with Einstein who was

also in Berlin in the 20s, so he missed his friends. In the end he was unhappy here and after three

years he decided to move back to his home country of Austria where he was given an appointment

at the University of Graz in Austria and also another appointment at the University of Vienna

and that’s where Schrödinger went. He’d left Berlin in 1933 because he wasn’t

very happy with the politics that was going on in Germany at the time. Science and politics in those days really

intermixed. He didn’t like what the Nazis were doing,

so he came to Oxford. But then he made the big mistake of going

to Austria and he didn’t realize that there were going to be problems in Austria because

Hitler’s troops marched in in 1938. Schrödinger had to escape from Austria. There was a worry he might even be arrested,

but he managed to escape and he went to live in the Vatican for a short period and then

he was contacted by the premier of Ireland, de Valera, who asked him to go and work in

Ireland. So Schrödinger actually managed to come back

here, to Magdalen College Oxford in 1938 and from there went to Ireland. He started at the Institute for Advanced Study

in Dublin in Ireland and there he did another very important piece of work. He was thinking about atoms and molecules

and he realized that the fundamental principles of physics and chemistry, including his quantum

mechanics, should be applied to the molecules of life, molecules like DNA and proteins which

were just emerging at that time in the late 1940s. So Schrödinger wrote a small book in Dublin

called ‘What is Life?’ that was stating that the basic principles of physics and chemistry

could be applied to biology. Now everybody knows that: the field of molecular

biology is explained by these basic principles, but in those times people haven’t really thought

about that. Some of the great young scientists of the

time, such as Watson and Crick, read his book and thought: I better get into molecular biology,

and that’s what they did. So you’ve got these great discoveries in the

1950s by people like Watson and Crick: the structure of DNA and then eventually after

that RNA and other biological molecules. All of these were inspired by Schrödinger’s

little book. So he was a remarkable person setting up the

basic quantum theory that underlies all the properties that we can observe essentially

of atoms and molecules and also starting the revolution in molecular biology that we’ve

seen to the present day. He was a hugely influential person. He wasn’t very popular: he wrote all of his

papers essentially on his own. Nowadays you have big research groups; Schrödinger

did it on his own. He was an individual person and never happy

where he was. He wasn’t very happy here in Magdalen College

Oxford, he did his original work actually in Zurich where he was just for a few years

in the early 1920s, and he wasn’t in Ireland for that long. After the Second World War he decided to go

back to Austria where he’d had the problems in the Hitler times. But he was welcome back to Austria as a hero:

they put his face on the banknotes and on the stamps, a crater on the Moon was named

after him and he became one of the great people of Austria at that time. But we still remember him here in Oxford,

we were very grateful that the great scientist Schrödinger came here. My own research is in quantum chemistry and

that is solving Schrödinger’s equations for atoms and molecules and particularly for chemical

reactions. So to me he is my scientific hero, and as

president of Magdalen College I work in this room, the place where Schrödinger heard he’d

won the Nobel Prize. That is really quite something.

First ?

Very interesting. Thank you for sharing your knowledge

How did this get into my pets feed?

Wow! Wow! I’ll bet he tells that story to every visitor. Thank you for telling it to us.

It would be better if he told about those equations