[jeffreyH (OP)]

I posted this link a while ago.
http://users.aber.ac.uk/ruw/teach/237/hatom.php
Any thoughts on the above? It is a pretty vague question. Sorry about that.

[timey]

https://physics.stackexchange.com/questions/69873/can-we-apply-schr%C3%B6dinger-equation-in-newton-gravitational-potential-and-derive-t

:above link
Note that this does not imply a quantization of the gravitational field. It is just a quantum particle in a classical, external, weak gravitational potential.

[PmbPhy]

I posted this link a while ago.
http://users.aber.ac.uk/ruw/teach/237/hatom.php
Any thoughts on the above? It is a pretty vague question. Sorry about that.

It depends on what you mean by "compatible with gravity." If you're asking if its valid if the Hamiltonian represents a gravitational field then yes. Otherwise I don't know what you're referring to.

[jeffreyH (OP)]

I will have to refer to Mr Hawking in order to proceed.
http://cds.cern.ch/record/275032/files/9501014.pdf

[PmbPhy]

I will have to refer to Mr Hawking in order to proceed.
http://cds.cern.ch/record/275032/files/9501014.pdf

That appears to be about quantum gravity, a field I'm not versed in. However I get the impression that the Hamiltonian in question is for the field and not for a particle. The Schrodinger equation in that case has nothing to do with it.

[jeffreyH (OP)]

I'm still planning on reading the PDF though. I think I need Legendre transformations to get from a Lagrangian to a Hamiltonian.