The Heisenberg Uncertainty Principle states that the product of two conjugates (e.g. space and momentum, or Energy and time) cannot be arbitrarily small (n particular, it cannot be smaller that the Plank constant).  And someone uses the Schrödinger wave equation : Hφ = V φ (where H is the Hamiltonian Operator and V is the potential operator) to prove the Heisenberg Uncertainty Principle.  We can either use the Heisenberg matrix to solve the Quantum Mechanics (in essence, we are using space of sequences, the square summable ones to be exact) or go into the square integrable space of functions to study the QM effect.  Some mathematicians realize that this Hibert Space is the same as the space of square summable space of sequences and that’s another neat way to look at elements of the state space.

So is light a particle or a wave?  Young’s double-slit experiment (and our intuition) suggested that light is a wave.  Einstein’s Nobel Prize winning photo-electric effect experiment suggested that it is a particle.  It’s both.  Or neither.  Or either!   Using electron in the Young’s double split experiment yielded the same result as using light.  That means to say it is proof that an electron is a wave. But many Physicists preferred that everything, not just electrons, is a wave.   Dr. deBroglie even go to the extend of giving all these seemingly “unwavy” particles  wavelengths and frequencies.  So you’re a wave.  I’m a wave and so is the earth and the ball we kick, etc.  If everything is wavy, then we all can be  Fourier analyzed?  That we all can be written as sums of sine and cosine waves?  As Fourier series?

This wave-particle duality is frequently the point where Science meet philosophy.  Examples of books written about this aspect (to name a few) are “The Tao of Physics” by Capra and the “The Dancing 物理 Masters” by Zukav.  In fact, if one is familiar with “色不異空，空不異色“ or “色即是空，空即是色”, the aspect of particle duality is frequently quoted.

And the Uncertainty Principle, for instance, if we know the particle’s velocity exactly, our mind has “transformed” the particle into one whose position is not known at all (or vice versa).  This is how many “religious practitioners” explained how we can be everywhere and at one with the universe.  and many times, the scientific/philosophical aspect will be stretched to explain “无眼耳鼻舌身意“ （no eye ear nose tongue body feel. ) This is also where the Schrodinger’s cat got it’s name in the proverb “curiosity kills the cat”.

Usually to bring this to a high point, Einstein EPR paradox and Quantum Entanglement are quoted. But these two are highly mathematical and thoretical, not many people have enough to even understand the theory, let alone compare and understand its implications in philosophy and religion.