Biggest experimental validations of postulates of Quantum Mechanics What are some experimental results that validate postulates of Quantum mechanics completely beyond any doubt ? Since there are alternate theories being used by various physicists to describe the same phenomena, I wonder there are some results that are with complete exclusion, described by Quantum Mechanical postulates ?
 A: There's no such thing as verifying a theory "to complete exclusion." One of the key principles of the scientific method is that theories can't be proven by experiment, only supported (or disproven as the case may be). The scientific reality is that quantum mechanics, like any other theory of its caliber, has been supported by countless experiments, so we assume, for all intents and purposes, that it's true. That's not the same thing as proving it's true.
The consequence of this as it pertains to your question is that there's no experiment that can disprove 100% of all the theories competing with quantum mechanics, since you can't prove quantum mechanics beyond a shadow of a doubt (the same way you can't 100% prove gravity, relativity, etc.). However, competing theories can be falsified on a case by case basis with experiments that show they make inaccurate predictions. So if you name specific theories that compete with quantum mechanics I can find experiments that disproved them.
A: Since the issue of considering theories as axiomatic has been raised
by @Ben Crowell as relevant to this question (given its title), I
think it needs some more discussion.
I do not quite agree with @Ben Crowell's statement regarding
postulates and axiomatization. Though postulates can be analyzed in
isolation, to understand their relations to various other postulates
(independence, contradiction, inferability), and axiomatic theory must
be analyzed as a whole.  The example of Playfair's axiom (actually
Proclus' axiom according to Wikipedia) supports this. Separated from
the other axioms of Euclidian geometry, Playfair's axiom is different
from the fifth postulate of Euclid since, with an appropriate set of
others postulates, they can lead to distinct theories.  However, with
the other postulates of Euclid, they both produce provably the same theory for Euclidian geometry.
Unicity or non-unicity of axiomatization is relevant only up to
logical equivalence.
The fact that there may be several axiomatizations of
quantum mechanics is not in itself an issue. The same is true of
Euclidian geometry (see above) or of calculabity, but there have been
proved equivalent. The real question is whether there are
axiomatizations (even incomplete ones) that are not equivalent, or
more precisely that are independent (since on theory could be a
consequence of another, the converse being false).
So a first question, if we consider axiomatizations of Quantum
Mechanics (and that would be true of any other theory) is whether the
different axiomatizations are equivalent or may lead to different
results which cannot yet be confirmed or falsified experimentally.
More precisely, a theory can be falsified by observation (though
observation can also be misinterpreted). But being confirmed by
observation does not guarantee that the theory will not be falsified
later.
Then the question of @user25957 must really be understood as: "are
there competing formalizations" (i.e., possibly partial
axiomatizations) that have been proved non equivalent, such that none
can be falsified with current knowledge, observational or experimental
evidence." Actually the situation can be worse if we come up with
theories for which we do not even know whether they are equivalent or
not. This does happen in mathematics, but I would conjecture that it
is rarer in physics. (Is it ?)
However the question is a bit ambiguous in part of its statement. Whether
one can "validate Quantum mechanics completely beyond any doubt"
clearly calls for a negative answer, if taken in an absolute sense,
as for any other theory in Physics.
But the question remains whether there are alternative formalizations
of the observed phenomena that are not equivalent, and may not yet be
falsified. Of course, it may be unreasonable to expect anyone to know
of all competing approaches in a very active field of research, and
the question could be unfair in that sense. It should probably be read
as: "are there well publicized (recognized ?) competing variations on
Quantum Mechanics formalization that are not equivalent and cannot yet
be distinguished by observational evidence".
A last point, more directly as an answer to the question, is that a
theory that has matured a long time, that has conformed a considerable
amount of observational evidence and withstood many predictive tests,
is seldom (not to say never) falsified in an absolute sense. Very
often the falsifying must be understood as finding the limits whithin
which the theory is an accurate representation of reality. Newton's
theories are not really falsified by the evidence supporting
Einstein's theories. It is only that Eistein has shown that things
become more subtle in some extreme contexts.  Actually, geocentric
theories of the universe, that predate Copernic and Gallileo, were
still very adequate afterwards for navigating the oceans on the
planet. It is largely a question of context and accuracy. The
speedometer of your car knows nothing of relativity theory.
So, after a century of remarquable results and confirmed predictions,
it is to be expected that quantum mechanics ir largely on very firm
ground. Physicist may find new (equivalent) ways of presenting it that
will make it easier to understand, to use and to build upon. That is
the normal course of science. But, having established for itself a
large domain of applicability where it is a confirmed and usable
theory, it will remain such in all likelyhood.  And hopefully for
physicists, there should be much more to be explored and understood.
