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# Quantum Mechanics ## What is quantum mechanics? Quantum mechanics is the science that deals with the physics of things smaller than we can see - atoms, electrons, quarks, etc. Quantum mechanics is weird. The rules that govern the quantum world are very different from the rules that govern the ev...

# Quantum Mechanics ## What is quantum mechanics? Quantum mechanics is the science that deals with the physics of things smaller than we can see - atoms, electrons, quarks, etc. Quantum mechanics is weird. The rules that govern the quantum world are very different from the rules that govern the everyday world. ### Classical vs Quantum | Classical Mechanics | Quantum Mechanics | | :--------------------------------------------- | :---------------------------------------------------------------------- | | Everyday objects (baseballs, cars, etc.) | Very small objects (atoms, electrons, etc.) | | Position and velocity can be known exactly | Position and velocity cannot be known exactly (Heisenberg Uncertainty) | | Energy can take on any continuous value | Energy is quantized (only certain values are allowed) | | Objects are either particles or waves | Objects can be both particles and waves (wave-particle duality) | | The world is deterministic (predictable) | The world is probabilistic (we can only predict probabilities) | ## Wave-Particle Duality One of the weirdest things about quantum mechanics is that objects can be both particles and waves. ### Particles Particles are objects that have a definite position and momentum. They are localized in space. Examples: baseballs, cars, electrons ### Waves Waves are disturbances that propagate through space. They are delocalized in space. Examples: water waves, sound waves, light waves ### "Proof" Young's Double Slit Experiment Shine light through two slits. The light will create an interference pattern on the other side. This shows that light is a wave. Now send electrons through two slits. The electrons will also create an interference pattern. This shows that electrons are also waves. ## Heisenberg Uncertainty Principle We can never know both the position and velocity of an object exactly. The more accurately we know the position, the less accurately we know the velocity, and vice versa. $$ \Delta x \Delta p \geq \frac{\hbar}{2} $$ Where: * $\Delta x$ is the uncertainty in position * $\Delta p$ is the uncertainty in momentum * $\hbar$ is the reduced Planck constant ($\frac{h}{2\pi}$) Implications: We can only predict the probability of finding a particle in a certain location. **Probability Density** The probability of finding a particle at a certain location is given by the square of the wave function. $$ P(x) = |\Psi(x)|^2 $$ Where: * $P(x)$ is the probability density * $\Psi(x)$ is the wave function ## Quantum Weirdness ### Quantum Tunneling Particles can pass through barriers even if they don't have enough energy to overcome them. ### Quantum Entanglement Two particles can be linked together in such a way that they share the same fate, no matter how far apart they are. ### Quantum Superposition Particles can be in multiple states at the same time.