physics

Per-Olov Löwdin

Per-Olov Löwdin is a physics topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Per-Olov Löwdin rather than just read about it. In short: Per-Olov Löwdin (October 28, 1916 – October 6, 2000) was a Swedish physicist, professor at the University of Uppsala from 1960 to 1983, and in parallel at the University of Florida until 1993. A former graduate student under Ivar Waller, Löwdin formulated in 1950 the symmetric orthogonalization scheme for atomic and molecular orbital calculations, greatly simplifying the tight-binding method.

Key takeaways

Per-Olov Löwdin belongs to physics; place it in that map before memorising details.
Learn the definition first, then one example that makes the definition concrete.
Connect Per-Olov Löwdin to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of Per-Olov Löwdin from memory before moving on to harder problems.

Reference excerpt

Per-Olov Löwdin (October 28, 1916 – October 6, 2000) was a Swedish physicist, professor at the University of Uppsala from 1960 to 1983, and in parallel at the University of Florida until 1993. A former graduate student under Ivar Waller, Löwdin formulated in 1950 the symmetric orthogonalization scheme for atomic and molecular orbital calculations, greatly simplifying the tight-binding method. This scheme is the basis of the zero-differential overlap (ZDO) approximation used in semiempirical theories. In 1956 he introduced the canonical orthogonalization scheme, which is optimal for eliminating approximate linear dependencies of a basis set. These orthogonalization procedures are widely used today in all modern quantum chemistry calculations. The famous 'Löwdin's pairing theorem' used in restricted open-shell Hartree–Fock (ROHF), unrestricted Hartree–Fock (UHF) and generalized valence bond (RES-GVB) theories is not his. According to himself, George G. Hall and King made the formal proposition after an informal suggestion by Löwdin. His Löwdin partitioning technique for quantum chemistry problems is best appreciated through the series of 14 papers on perturbation theory published between 1963 and 1971. He was also a very active teacher, starting the Summer Schools of Quantum Chemistry at Uppsala around 1958. In 1959 and 1960, Löwdin started the Quantum Theory Project at the University of Florida as a sister project to the Uppsala Quantum Chemistry Group. In 1964 he was joined by John C. Slater from MIT. The International Winter Institutes (held initially at Sanibel Island, and later at Gainesville) provided the initiation into quantum chemistry for hundreds of young Latin American scientists during the 1980s and 1990s. In 1960 he founded the Sanibel Symposium in conjunction with the Winter Institute, held every year since then. Löwdin was elected a member of the Royal Swedish Academy of Sciences in 1969, the American Philosophical Society in 1983, and was a member of the committee for the Nobel Prize in Physics from 1972 to 1984. He was the founder of the International Journal of Quantum Chemistry and of the series Advances in Quantum Chemistry. He was a foundation member of the International Academy of Quantum Molecular Science.

Publications

References

External links Linderberg, Jan (2003). "Biographical Memoir" (PDF). Proc. Am. Philos. Soc. 147 (2): 175–180. Archived from the original (PDF) on 2016-04-11. Retrieved 2016-02-12. "Per-Olov Löwdin Curriculum Vitae". International Journal of Quantum Chemistry. 90 (1): 1–11. 2002. doi:10.1002/qua.10096. Kimio Ohno Early Ideas in the history of Quantum Chemistry (1976) The Löwdin Lectures, Uppsala University Quantum Theory Project founded by Löwdin at the University of Florida in 1960

Worked examples

Example 1 — a first encounter with Per-Olov Löwdin

Start with the simplest possible case. Write down what Per-Olov Löwdin claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In physics, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Per-Olov Löwdin before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Per-Olov Löwdin ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Per-Olov Löwdin

In research: Per-Olov Löwdin appears in physics research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses Per-Olov Löwdin in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: Per-Olov Löwdin is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1916 births, 2000 deaths, Academic staff of Uppsala University, so understanding it makes those chapters shorter.
In everyday life: Look for Per-Olov Löwdin outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

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How to study Per-Olov Löwdin in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Per-Olov Löwdin means in your own words.
Compare your version with the excerpt and mark what you missed.
Work through the three examples above with pen and paper.
Explain Per-Olov Löwdin out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Per-Olov Löwdin in simple terms?

Why does Per-Olov Löwdin matter?

Because it connects several physics ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Per-Olov Löwdin?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Per-Olov Löwdin.