Shouldn't phi at 17:21 for an example be only +i/hbar * ...? Then in the last equation, C+ * e^i*phi + C_ e^-i*phi will give the sine and cosine, but now only with phi = + i/hbar * ..., avoiding getting 2 different psi functions, one for positive phi and one for negative.
Not sure what you are asking. The constants are complex and so this is a very general solution. It is stating that it is possible to express a general oscillating function with either complex exponentials of sines and cosines. The constants are completely general.
@@iitenergymaterialsgroup4816 I meant that the phi should only have the positive part at 17:21 and not both positive and negative since it'd lead to two different sine and cosine expressions? Sorry for the confussion by the way, and thank you for replying!
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Shouldn't phi at 17:21 for an example be only +i/hbar * ...? Then in the last equation, C+ * e^i*phi + C_ e^-i*phi will give the sine and cosine, but now only with phi = + i/hbar * ..., avoiding getting 2 different psi functions, one for positive phi and one for negative.
Not sure what you are asking. The constants are complex and so this is a very general solution. It is stating that it is possible to express a general oscillating function with either complex exponentials of sines and cosines. The constants are completely general.
@@iitenergymaterialsgroup4816 I meant that the phi should only have the positive part at 17:21 and not both positive and negative since it'd lead to two different sine and cosine expressions? Sorry for the confussion by the way, and thank you for replying!
My point is that the constants are totally general and can compensate for signs.
Wouldn't a free particle have potential 0? Our potential is constant but it is nonzero.
A constant potential is the same as zero. You can simply shift it. The important quantity is the energy of the particle relative to the potential.
@@iitenergymaterialsgroup4816 thank you :)
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