If you shift the wave function by phase angle delta in order to get a continuous wave, then at the merging point the two connected wave functions wont have the same derivative. I dont think you could really do this that way, dont you?
+Zhardamon That is a good point because if the amplitudes of each wave are the same but they're frequencies are different, then it would seem that the r values at which the derivatives are the same, there would be a discontinuity in the wave function. Likewise, the r values at which the wave functions has the same value, there derivatives would be different and thus there would be a sharp turn. Since it is obvious that the frequencies are different, I think that the only way out of this is to conclude that the amplitudes must be different. This way you could choose each wave amplitude so that, at the r value in question, the functional values and derivatives are both the same. And I think, indeed, that is how the differential equation is solved.
Wonderful Lecture. Thankyou
Thanks, clear and straightforward
If you shift the wave function by phase angle delta in order to get a continuous wave, then at the merging point the two connected wave functions wont have the same derivative. I dont think you could really do this that way, dont you?
+Zhardamon That is a good point because if the amplitudes of each wave are the same but they're frequencies are different, then it would seem that the r values at which the derivatives are the same, there would be a discontinuity in the wave function. Likewise, the r values at which the wave functions has the same value, there derivatives would be different and thus there would be a sharp turn.
Since it is obvious that the frequencies are different, I think that the only way out of this is to conclude that the amplitudes must be different. This way you could choose each wave amplitude so that, at the r value in question, the functional values and derivatives are both the same. And I think, indeed, that is how the differential equation is solved.
Really enjoyable videos, I did ohysics at A levels and got an A (no A stars back then) and I had a similar teacher to you. Thanks.
thank you sir!!
Thanks sir..
First!