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I'm coming here from going through the Dirac delta potential in QM to clear my mind about the case when E < 0, which as a result produces the single bound state solution in that potential. The thing that's vexing my soul(if we have one anyways) is the fact that a particle is taken to be in possession of negative energy. Mathematically speaking, how can it be that a particle has negative energy if both the energy that's coming from the kinetic term and that of the potential are strictly positive? Physically speaking, how can it be that a particle possesses negative energy if it exists in this universe at all? Even if it hasn't got any momentum there's potential. And unless you're analyzing it's motion relative to a reference frame (easiest example would be to pick the ceiling as the point where the gravitational potential is zero therefore an immobile body in the room would end up with negative energy), you can't have a particle of negative energy. Even then, it's because of relativity and not the actual true energy and Introduction to QM by Griffiths(any intro textbook to qm for that matter) doesn't take relativity into account. A particle can't actually POSSESS negative energy and exist realistically at the same time I don't think.

I am truly sorry to discuss such petty matter in this forum but I don't have any professor to go to and talk QM with because I'm still 16 attending high school. This kind man deriving the ddf potential bound state solution to Shroed's on youtube circumvents my problem by setting the ddf to ping to -∞ so that by having E < 0 the bound state just mathematically comes by. I thank anyone in advance for any enlightment they can offer :D

I am truly sorry to discuss such petty matter in this forum but I don't have any professor to go to and talk QM with because I'm still 16 attending high school. This kind man deriving the ddf potential bound state solution to Shroed's on youtube circumvents my problem by setting the ddf to ping to -∞ so that by having E < 0 the bound state just mathematically comes by. I thank anyone in advance for any enlightment they can offer :D

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