Lecture 1 - Quantum Basics

# Stern - Gerlach experiment

Rajarshi Tiwari

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## Slide 1: Linear Algebra
- Vector independence 
- Span and dimension 
- Equation: $a \mathbf{v}_1 + b \mathbf{v}_2 = 0$

$$
\sqrt{\pi} = \int_{-\infty}^{\infty} e^{-x^2} dx
$$

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## Columns

**Left column**

- Point A
- Point B

</div>
<div style="flex: 1;">

**Right column**
$$
H = \sum_{ij} t_{ij} c_i^\dagger c_j + \text{h.c.}
$$
</div>
</div>

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## Slide 2: Quantum Mechanics
Hilbert space grows as $2^n$ with number of qubits $n$.

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## Slide 3: Greek Letters
$\alpha x^2 + \beta y^2 = \gamma z^2$

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## Slide 4: Code Highlighting

```python [1-2|4]
def quantum_state(n):
    # wavefunction
    return f"Ψ_{n}"

print(quantum_state(1))
```

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- 👉 Each `---` = new slide.

- 👉 Each `--` = vertical sub-slide under same topic.
  - Think of it as **2D** navigation through slides.

- 👉 Inline LaTeX with `$...$` and block math with `$$...$$`.

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# Example with CSS columns

<div class="cols">
  <div class="col">
    <h3>Left</h3>
    <ul>
      <li>Point A</li>
      <li>Point B</li>
    </ul>
  </div>
  <div class="col">
    <h3>Right</h3>
    <p>Diagram:</p>
    <img src="diagram.png" style="max-width:100%">
  </div>
</div>

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## Mermaid graph

<div class="mermaid">
graph LR
  A ---> B & C ----> D & E & F ---> G ---> Z
</div>

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# Thank you!