Norbert Wiener’s biography describes how Heisenberg was likely present when he spoke on his foundational work on harmonic analysis - which contains closely analogous results of course - during his visit to Göttingen in 1926. It’s a tantalizing historical anecdote about the origins of the uncertainty relation, but I don’t believe I have ever seen it securely documented.
That's a great video! I'm on the way to my physics bachelor and am taking a QM class this semester. I stumbled upon this video on my journey to find literature, papers or anything that would show or explain the maths on how we go from schrödinger to heisenberg or rather how that term on the right hand side disappears. I do know that in symmetric states on average its zero but thats what a fellow student told me and as I said I can't find anything evaluating that further. I feel dumb but your help by explaining that would be so appreciated. :)
Glad you liked the video! You might find this paper useful: arxiv.org/pdf/physics/0105035. It's a paper that gives a survey of the Schrödinger Uncertainty Relation (along with Heisenberg's + Robertson's). It discusses in detail how all 3 relations are related as well as the physical relevance of Schrödinger's to squeezed states of light. Let me know if you have any specific questions!
Schrödinger on Heisenberg “After matrices are thus constructed in a very general way, so as to satisfy the general rules, I will show the following in Section 4. The special system of algebraic equations, which, in a special case, connects the matrices of the position and impulse co-ordinates with the matrix of the Hamiltonian function, and which the authors call “equations of motion”, will be completely solved by assigning the auxiliary role to a definite orthogonal system, namely, to the system of proper functions of that partial differential equation which forms the basis of my wave mechanics.” On the Relation of the Quantum Mechanics of Heisenberg, Born, and Jordan, and that of Schrödinger. Anallen der Physik (4), vol. 79, 1926. English, 1928 Blackie and Sons LTD..
Generalized uncertainty principle, wow, learned something new. Thanks.
you're welcome!
Norbert Wiener’s biography describes how Heisenberg was likely present when he spoke on his foundational work on harmonic analysis - which contains closely analogous results of course - during his visit to Göttingen in 1926. It’s a tantalizing historical anecdote about the origins of the uncertainty relation, but I don’t believe I have ever seen it securely documented.
That's a great video! I'm on the way to my physics bachelor and am taking a QM class this semester. I stumbled upon this video on my journey to find literature, papers or anything that would show or explain the maths on how we go from schrödinger to heisenberg or rather how that term on the right hand side disappears. I do know that in symmetric states on average its zero but thats what a fellow student told me and as I said I can't find anything evaluating that further. I feel dumb but your help by explaining that would be so appreciated. :)
Glad you liked the video! You might find this paper useful: arxiv.org/pdf/physics/0105035.
It's a paper that gives a survey of the Schrödinger Uncertainty Relation (along with Heisenberg's + Robertson's). It discusses in detail how all 3 relations are related as well as the physical relevance of Schrödinger's to squeezed states of light.
Let me know if you have any specific questions!
Schrödinger on Heisenberg
“After matrices are thus constructed in a very general way, so as to satisfy the general rules, I will show the following in Section 4. The special system of algebraic equations, which, in a special case, connects the matrices of the position and impulse co-ordinates with the matrix of the Hamiltonian function, and which the authors call “equations of motion”, will be completely solved by assigning the auxiliary role to a definite orthogonal system, namely, to the system of proper functions of that partial differential equation which forms the basis of my wave mechanics.”
On the Relation of the Quantum Mechanics of Heisenberg,
Born, and Jordan, and that of Schrödinger.
Anallen der Physik (4), vol. 79, 1926.
English, 1928 Blackie and Sons LTD..