Talk:Hamilton–Jacobi equation

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Interesting article for future consideration.

An anonymous editor recently added content about a new article on the quantum limit of the Hamilton-Jacobi equation. Here is the content, edited to remove time ref and to correct the reference:

For time-independent potentials, the Hamilton-Jacobi equation can be shown to be equivalent to the Schrödinger equation using only the linearly independence of the function $\psi$ and $\psi ^{*}$ , its complex conjugate. REF: Bulnes, J. D., et al. "From the Hamilton-Jacobi equation to the Schrödinger equation and vice versa, without additional terms and approximations." Himalayan Physics 11 (2024).

We need to wait for the content to be reference by a secondary source or to gain additional independent citations, per our policy on verification. Johnjbarton (talk) 14:56, 25 August 2024 (UTC)[reply]

"HJE" listed at Redirects for discussion

The redirect HJE has been listed at redirects for discussion to determine whether its use and function meets the redirect guidelines. Readers of this page are welcome to comment on this redirect at Wikipedia:Redirects for discussion/Log/2024 October 2 § HJE until a consensus is reached. 1234qwer 1234qwer 4 17:05, 2 October 2024 (UTC)[reply]

Conflation of action functional and Hamilton's principal function

The article claims that "The solution of the equation is the action functional, ⁠ S, called Hamilton's principal function in older textbooks." That's misleading at best and arguably just wrong: The action functional is, as the name suggests, a functional of a given system trajectory. In contrast, Hamilton's principal function is a function on phase space - its arguments are points, not curves. These are different (but related) mathematical objects. — Preceding unsigned comment added by 2003:C8:AF3B:7D00:48D9:80A4:7E9:778D (talk) 18:24, 1 January 2025 (UTC)[reply]

Unfortunately the terminology in this area is inconsistent. I checked the source, Hand and Finch and edited the content to match the source more closely. If you have other sources we may need to make further adjustments. Johnjbarton (talk) 23:22, 1 January 2025 (UTC)[reply]