I mentioned previously Schrödinger's interest in the Vedanta philosophy of Hinduism.
I found another eminent quantum physicists, Eugene Paul Wigner, who also had an interest in the Vedanta.
Wigner wrote on Sri Ramakrishna:
The waves of religious thought rise and fall, and on the topmost one stands the prophet of the period. Ramakrishna came to teach the religion of today, constructive, not destructive. He had to go afresh to nature to ask for facts, and he got scientific religion which never says "believe," but "see." "I see and you too, can see"---said Vivekananda.
Until not many years ago, the existence of a mind or soul would have been passionately denied by most physical scientists. The brilliant success of mechanistic and, more generally, macroscopic physics, and of chemistry, overshadowed the obvious fact that thoughts, desires, and emotions are not made of matter and it was nearly universally accepted among physical scientists that there is nothing besides matter.
The Wigner's friend paradox is at the origin of the theory that it is consciousness that causes a quantum wave to collapse (but that idea is still very controversial):
Consciousness causes collapse is the theory that observation by a conscious observer is responsible for the wavefunction collapse in quantum mechanics. It is an attempt to solve the Wigner's friend paradox by simply stating that collapse occurs at the first "conscious" observer. Supporters claim this is not a revival of substance dualism, since (in a ramification of this view) consciousness and objects are entangled and cannot be considered as separate. The consciousness causes collapse theory can be considered as a speculative appendage to almost any interpretation of quantum mechanics and most physicists regard it as a non-scientific concept, claiming that it is 1) unverifiable and 2) introduces unnecessary elements into physics.
It has been claimed that the theory meshes well with ancient Eastern mysticism and philosophy, including that of Buddhism which includes a belief in the transitory, interconnected nature of all things and the illusion of separation of thought and existence. This is one of the major themes of the book The Dancing Wu Li Masters. It also meshes well with the views of the New Thought movement.
The view is also presented in the popular and controversial documentaries What the Bleep Do We Know!? and The Secret,
Note the added emphasis: not so long ago, scientists would have denied that anything beside matter exist. But we know now that matter is mostly made of emptiness and a bunch of sub-atomic particles whose behaviour is really bizarre. Now, scientists do not deny the existence of a soul or non-physical (non-material) consciousness. They merely say that is is not provable and thus conveniently brush the idea under the carpet.
I am happy with the scientist keeping the soul out of their equations. What I would like, though, is that the scientists on one side, the mystics on the other, and the rest of us in the middle be clear on the fundamental difference between the realms investigated by the two groups: to the scientist, the physical 3D world, to the mystics everything beyond that.
Thus, the idea is not to use science to prove or disprove the existence of a soul, but to understand that it is not necessarily its job to do so.