https://seunghoonchoi.com/tags/exams/Recent content in Exams on Seunghoon ChoiHugoen-USSat, 27 Jun 2026 22:55:00 +0900https://seunghoonchoi.com/column/questions-lifeline/Sat, 27 Jun 2026 22:55:00 +0900https://seunghoonchoi.com/column/questions-lifeline/<p><img src="https://seunghoonchoi.com/images/col-questions-lifeline-opt.jpg" alt="A teacher lectures at a quantum mechanics board while one student among many feels overwhelmed by unanswered questions"></p> <p class="inline-image-caption">Many questions may mean not that understanding is slow, but that the person does not skip parts they have not understood.</p> <p>When I studied quantum mechanics in engineering school, equations like these appeared on the board first.</p> <div class="formula-block"> <math display="block" xmlns="http://www.w3.org/1998/Math/MathML"> <mrow><mover accent="true"><mi>H</mi><mo stretchy="false">^</mo></mover><mi>ψ</mi><mo>=</mo><mi>E</mi><mi>ψ</mi></mrow> </math> <math display="block" xmlns="http://www.w3.org/1998/Math/MathML"> <mrow><mover accent="true"><mi>H</mi><mo stretchy="false">^</mo></mover><mo>=</mo><mo>-</mo><mfrac><msup><mi>ℏ</mi><mn>2</mn></msup><mrow><mn>2</mn><mi>m</mi></mrow></mfrac><msup><mi>∇</mi><mn>2</mn></msup><mo>+</mo><mi>V</mi><mo stretchy="false">(</mo><mi>r</mi><mo stretchy="false">)</mo></mrow> </math> <math display="block" xmlns="http://www.w3.org/1998/Math/MathML"> <mrow><mo stretchy="false">⟨</mo><mi>φ</mi><mo stretchy="false">|</mo><mi>ψ</mi><mo stretchy="false">⟩</mo><mo>=</mo><mo>∫</mo><msup><mi>φ</mi><mo>*</mo></msup><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo><mi>ψ</mi><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo><mi>d</mi><mi>x</mi></mrow> </math> </div> <p>The class was explaining physical phenomena, but what reached my eyes first was unfamiliar mathematical notation. Hamiltonian, wave function, eigenvalue, operator, bra-ket notation. These words appeared, and at some point the notation was being used as if it were already a language everyone knew.</p>