Applications of quantum mechanics include the laser , the transistor , the electron microscope , and magnetic resonance imaging. This implied that the property of the atom that corresponds to the magnet's orientation must be quantized, taking one of two values either up or down , as opposed to being chosen freely from any angle. The video about the fundamentals of electromagnetism. For example, the uncertainty principle of quantum mechanics means that the more closely one pins down one measurement such as the position of a particle , the less accurate another complementary measurement pertaining to the same particle such as its speed must become. The modern theory is formulated in various specially developed mathematical formalisms. Principles of Quantum Mechanics. In , Heisenberg proved that this last assumption is not correct. This result, which is clearly wrong, is known as the ultraviolet catastrophe.