I think Akira has described the current difficult situation in modern Physics. I could add that quantization is merely a linear algebraic concept (just like all tensors and derivatives that we are using without even a simple proof for existence) inside a rather non linear world. My small advice: don't screw up your future with topics that:
everybody accepts in a private discussion that is a mess
nobody accepts an alternative theory in a public discussion
QM Proves phase velocity can be exceed than the speed of light. Whereas phase velocity has no significance in QM. In QM one determine group velocity (velocity of Wave packet associated with particle) which can not exceed than speed of light.
Through the fact that, in the presence of gravity, it isn't, in general, possible to define a unique vacuum state. As noted above, this is the essence of Hawking's calculation and was generalized by Unruh. However it's wrong to focus on the ``Schrödinger wavefunction''-the property in question is a feature of any formulation of quantum mechanics. Indeed, its origin lies in the local symmetries of classical gravity, that imply that conserved quantities can only be defined on the boundary of the spacetime and are observer-dependent, in the absence of globally defined Killing vectors.
The Schrodinger wave function has a probabilistic indeterministic meaning, while gravity has deterministic nature. Even if gravity affected the wave function, in that case only the values of probability would change. It is known nevertheless the probabilistic descriptions of physical events are unsatisfactory and the behavior of elementary massive particles into a gravitational field can be understood and described by other more satisfactory methods.
One of the conditions used by Schrödinger to formulate his wave equation, using a plausibility argument, included the expression E = K + V where E is the total energy of the particle, K is the kinetic energy and V the potential energy. E is a constant in this argument and so there can only be a transfer between kinetic and potential energies as the velocity of the particle changes. The expression used by Schrödinger for the kinetic energy term was non-relativistic, however in 1928 Dirac developed a relativistic theory of quantum mechanics utilising essentially the same postulates as the Schrödinger theory however incorporating a relativistic element (ref: Section 7.2.2 Schrödinger Equations, Physics in 5 Dimension, pages 128 - 133).
The expression E = K + V, using the same definition of terms as given above, appears again in connection with the theme “motion in 5-dimensional space produces particle and large body motion typically associated with attractive forces in classical physics”. The theory of motion in 5-dimensional space accounts for the behaviour of electrons in atoms, as well as nucleons forming nuclei and planets orbiting the Sun. The universal equations of motion work in all cases and the energy of all objects remain constant in their own frame of reference (ref: Chapter 16 - Motion in 5-dimensional local space is Gravity, Physics in 5 Dimension, pages 394 - 457).
So the Schrödinger wave function is based on an expression of energy that is also fundamental to the equations of motion of particles and bodies in a 5-dimensional local space producing gravity like behaviour (attractive force). However, in the theory of physics in 5-dimensions, the orbiting motion of particles and bodies alike is not due to attractive forces (e.g. gravity) but arises from the hypothesis that “All particles and bodies move along closed paths (an orbit) with a common constant velocity c and have intrinsic values of angular momentum” (ref: Section 10.1 – Hypothesis: Closed Paths in Space, Physics in 5 Dimension, pages 192 – 193).
Therefore we should look for theories of physics that use common expressions of energy for the many fields of physics where E = K + V in all cases. Physics in 5 dimensions is just one such theory and there may be others. The Schrödinger wave function and the effect of “gravity” should be using common expressions of energy and common equations of motion for all particles and bodies in local spaces (e.g. electrons orbiting nuclei or the earth orbiting the sun).
Gravity doesn’t affect the Schrödinger wave function; it is a fundamental part of the Schrödinger wave function.
Alan
PS: The above 5-dimensional space energy expression is entirely consistent and compatible with Einstein’s 4-dimensional space energy expression (Section 5.3.3 - 4- and 5-dimensional space energy expressions are compatible, Physics in 5 Dimension, page 48).
For the full text of the references given for Physics in 5 Dimensions – see https://www.researchgate.net/publication/266794606_Physics_in_5_Dimensions_Bye_bye_Big_Bang
The two-body problem is certainly quantizable in the non-relativistic case (a standard exercise in quantum mechanics) and for the Coulomb potential the work of Pauli and Fock showed how the quantum potential is bounded from below. Experiments with cold neutrons have, in fact, measured the energy levels in a Newtonian gravitational potential a couple of years ago. However this isn't what's at issue here.