When I can I prefer to be lazy. 😊 The work to find can be avoided with a foresighted symmetry argument: Reflecting the problem around the point a/2 changes nothing in the setup. This action must then leave the solution unaffected too. With the caveat that the eigenfunctions can pick up a phase factor after reflection (like an antisymmetric solution would). However, when squared any phase factor disappears, and all position probability densities will be symmetric around a/2. Therefore = a/2 for all n. Note that there is an asterisk for problems containing degenerate eigenvalues: Then a (degenerate) eigenstate can change more than with a simple phase factor, but the space spanned by the all of it's related degenerate solutions will be unaffected. Anyway, there are no degenerate eigenvalues here so it's nice and easy.
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Keep it coming! I've been subbed for many years, your vids are top-notch!
Legend is backk! And now, Differential Geometry's era begins! :)
@@PunisherTR In that case, your wish will be granted! Next Monday I'll have a Differential Geometry video ready!
@@FacultyofKhan 🥹
@@FacultyofKhan let's go !!!
Here it is!
ruclips.net/video/VgKbxVSbDqI/видео.html
When I can I prefer to be lazy. 😊 The work to find can be avoided with a foresighted symmetry argument: Reflecting the problem around the point a/2 changes nothing in the setup. This action must then leave the solution unaffected too. With the caveat that the eigenfunctions can pick up a phase factor after reflection (like an antisymmetric solution would). However, when squared any phase factor disappears, and all position probability densities will be symmetric around a/2. Therefore = a/2 for all n.
Note that there is an asterisk for problems containing degenerate eigenvalues: Then a (degenerate) eigenstate can change more than with a simple phase factor, but the space spanned by the all of it's related degenerate solutions will be unaffected. Anyway, there are no degenerate eigenvalues here so it's nice and easy.
Appreciate the added insight!
Thank upu thank you thank you... this is on my test a week from now... also if you could drop a video on hydrogen that would be great
What software do you use to write in your videos?
sin(x)^2 = (1-cos(2x))/2
sin(x)cos(x)=sin(2x)/2
Just wondering why you didn't use the above identities!
Thank you for making Heisenberg happy 😊
Might as well get some integration/algebra practice while we're at it lol
@@FacultyofKhan your knowledge domain is quite vast. Congrats on your achievements.
Just thank you,
Could you please tell me What software do you use for writing.