Skip to main content
MathOverflow

Return to Answer

added 740 characters in body
Source Link
Mark Lewko
Mark Lewko
  • 13k
  • 1
  • 55
  • 87

ThisThis is true. This was proved by Hardy and Littlewood and the proof is reproduced in Zygmund's Trigonometric Series (which I don't have access to at the moment).

(Contradicting my prior "answer")

The answer to this question is truenegative. This was proved by Hardy and LittlewoodSuch counterexamples are known as "Pauli partners" and the proof is reproducedare studied in Zygmund's Trigonometric Series (which I don't have access to at, among other places, the momentquantum mechanics literature.

See, for example:

(J. V. Corbett and C. A. Hurst) Are Wave Functions Uniquely Determined by their position and momentum distributions? [https://www.cambridge.org/core/services/aop-cambridge-core/content/view/228E4A34D0B3C63C54B1A01006278C42/S0334270000001569a.pdf/are-wave-functions-uniquely-determined-by-their-position-and-momentum-distributions.pdf]

(P. Jaming) Phase Retrieval Techniques for Radar Ambiguity Problems [https://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.521.4906&rep=rep1&type=pdf]

This is true. This was proved by Hardy and Littlewood and the proof is reproduced in Zygmund's Trigonometric Series (which I don't have access to at the moment).

This is true. This was proved by Hardy and Littlewood and the proof is reproduced in Zygmund's Trigonometric Series (which I don't have access to at the moment).

(Contradicting my prior "answer")

The answer to this question is negative. Such counterexamples are known as "Pauli partners" and are studied in, among other places, the quantum mechanics literature.

See, for example:

(J. V. Corbett and C. A. Hurst) Are Wave Functions Uniquely Determined by their position and momentum distributions? [https://www.cambridge.org/core/services/aop-cambridge-core/content/view/228E4A34D0B3C63C54B1A01006278C42/S0334270000001569a.pdf/are-wave-functions-uniquely-determined-by-their-position-and-momentum-distributions.pdf]

(P. Jaming) Phase Retrieval Techniques for Radar Ambiguity Problems [https://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.521.4906&rep=rep1&type=pdf]

Source Link
Mark Lewko
Mark Lewko
  • 13k
  • 1
  • 55
  • 87

This is true. This was proved by Hardy and Littlewood and the proof is reproduced in Zygmund's Trigonometric Series (which I don't have access to at the moment).