Exploring Wavefunction Collapse in Quantum Mechanics

An SO(2,2) Iterated Function System Part 3 - Weyl spinors and null vectors In the early 1960s, Penrose was deeply preoccupied with a fundamental problem in physics: how to describe the geometry of spacetime in a way that naturally incorporated quantum mechanics and the behavior of light. https://lnkd.in/ewC72vNw

✨ Day 7 – QuCode 21 Days Challenge with QuCode ✨ Quantum Mechanics Basics At the heart of quantum theory lie three key ideas: • Schrödinger Equation: Describes how a system’s wave function evolves with time. • Measurement: Outcomes are probabilistic, and observation “collapses” the wave function into a definite state. • Postulates of QM: Define the rules of states, evolution, measurement, and how systems combine — the foundation of modern quantum science. Quantum mechanics reshapes how we think about reality: not deterministic, but deeply probabilistic and full of fascinating possibilities. #QuCode #QuantumComputing #SelfLearning

🎯 Day 7 of QuCode 21 Days Challenge : 🔬 Today I learned about the Schrödinger Equation, the core of quantum mechanics. It describes how a quantum state changes over time. Just like Newton’s laws explain motion in classical physics, Schrödinger’s equation explains the evolution of quantum systems. 🌊 This change in states can be linked to the wave nature of particles → a quantum particle behaves like a wave, and its state evolves smoothly according to the equation. 📌 Quantum Mechanics Postulates (simplified): 1. A system is represented by a state vector |ψ⟩ in Hilbert space. 2. Observables (like position, momentum, energy) are represented by operators. 3. Measurement outcomes are eigenvalues of those operators. 4. The state evolves over time using the Schrödinger equation. 👉 In short: The Schrödinger equation is the rulebook for how quantum states evolve — the foundation of quantum computing and quantum mechanics. #21DaysChallenge #QuantumComputing #SchrodingerEquation #QuantumMechanics #QuCode

𝐃𝐚𝐲-𝟑 𝐨𝐟 𝐐𝐮𝐚𝐧𝐭𝐮𝐦 𝐂𝐨𝐦𝐩𝐮𝐭𝐢𝐧𝐠 𝐂𝐡𝐚𝐥𝐥𝐞𝐧𝐠𝐞 | 𝐐𝐨𝐡𝐨𝐫𝐭-𝟑 𝐨𝐟 𝐐𝐮𝐚𝐧𝐭𝐮𝐦 𝐋𝐞𝐚𝐫𝐧𝐢𝐧𝐠 🚀QuCode Today’s focus was on Quantum vs Classical Mechanics — exploring how the quantum world fundamentally differs from classical physics in describing nature. Key topics explored: Determinism vs Probability Superposition and Measurement Quantum Entanglement vs Classical Correlation Wavefunction and State Space Understanding these differences is crucial for appreciating why quantum computing is so powerful compared to classical approaches. Excited to continue diving deeper into the quantum world in the days ahead! #QuCode #QuantumComputing #LearningChallenge #Day3 #QuCode #21DayChallenge #ContinuousLearning

🚀 Day 7 of the 21 Days Challenge with QuCode Today we explored one of the most fundamental pillars of quantum mechanics — the Schrödinger Equation ⚡. 🔹 Recalling the Basics Started with Newton’s Second Law to connect classical mechanics to quantum mechanics. Broke down every term in the Schrödinger wave equation. Understood that total energy (E) = kinetic energy + potential energy — ensuring conservation of energy. 🔹 Probability & Normalization Realized the wave function (Ψ) represents the probability of finding a particle in a given state. Learned about normalization conditions — keeping the probability conserved. Explored what it means for a wave function to collapse. 🔹 Operators & Evolution Studied the role of the Hamiltonian operator — the generator of energy and time evolution in quantum systems. Connected Hamiltonian eigenvalues & eigenvectors to measurable quantities. Understood why the equation uses complex numbers: to preserve probability and consistency across time. 👉 Key takeaway: The Schrödinger Equation isn’t just math — it’s the heart of quantum mechanics, describing how quantum systems evolve in time. It bridges physics, probability, and reality itself. 🌌 #21DaysChallenge #Qucode #QuantumMechanics #SchrodingerEquation #Hamiltonian #LearningJourney

🚀 Day 7 complete – QuCode 21 Days Quantum Computing Challenge Today’s deep dive: The Schrödinger equation – the backbone of quantum mechanics, describing how quantum states evolve with time. Measurement – unlike classical physics, we can’t pinpoint outcomes. Instead, the wave function tells us the probabilities of different results. The act of measurement itself changes the state. The postulates of quantum mechanics – from state representation to time evolution and measurement, they set the framework of the entire theory. Every day it feels clearer why quantum computing rests on these foundations it’s not just math, it’s a new way of thinking about physical reality. #Day7 #QuantumComputing #SchrodingerEquation #Measurement #QuantumMechanics #QuCode

🚀 Day 6 of the 21-Days Quantum Challenge with #QuCode Today’s focus: 🔹 Bra-Ket Notation 🔹 Operators 🔹 Basis States We explored why linear functions are so fundamental in Quantum Mechanics. The Bra <Q| is simply the flipped version of the Ket ∣P⟩, and its role as a linear functional is equivalent to taking an inner product. The beauty of Dirac’s bra-ket notation lies in how naturally it incorporates the Riesz Representation Theorem. Quantum states ψ live in an abstract space known as a Hilbert space. For example, spin-up and spin-down states (describing a single particle) live in a 2-dimensional Hilbert space. This means we can represent quantum particles in two equivalent ways: ✨ as wave functions ✨ as state vectors Loving how these abstract mathematical tools give us such a powerful lens into the quantum world. 🌌⚛️

DAY 5/21 - QC Just dove deep into the fascinating concept of tensor product state spaces in quantum mechanics! We all know that state spaces help describe individual quantum particles and their degrees of freedom. But what happens when we want to represent multiple degrees of freedom simultaneously—like three physical dimensions, spin, and orbital properties—or even systems composed of multiple particles? That’s where tensor product state spaces come into play. Instead of simply stacking components side by side, these spaces provide a powerful mathematical framework to combine individual state spaces into a single, more complex system. Interestingly, some quantum systems behave like straightforward combinations of their parts. Others—much more intriguing—cannot be reduced to such simple combinations, giving rise to the famously mysterious entangled states. This journey opened my eyes to how quantum mechanics stretches beyond intuition, requiring new math tools to truly capture the richness of multi-particle systems. Excited to explore more about entanglement next! Quantum physics is truly a mesmerising blend of math and mystery! #QUCODE #QC #HAPPYLEARNING

🎯 Day 11 of QuCode 21DaysChallenge : Today I explored some fascinating ideas about the foundations of quantum mechanics. Back in school, we learned physics as deterministic — if we know the present, we can predict the future. But quantum mechanics tells a different story. 1️⃣ Bohr & Schrödinger → Showed that at the quantum level, the universe is probabilistic (non-deterministic). A particle doesn’t have a fixed state until we measure it. 2️⃣ EPR Paradox (Einstein, Podolsky, Rosen) → They disagreed, suggesting there must be hidden local variables that make the universe deterministic — we just don’t see them. 3️⃣ Bell’s Theorem & Inequality → John Bell proposed a test. If hidden variables were real, the inequality would hold. But experiments showed it is violated. ✨ Conclusion: Quantum mechanics wins → particles don’t have definite states before measurement. The quantum world is fundamentally non-deterministic. 👉 It’s very interesting to dive deeper into physics we once studied in our school classroom — now seeing how it challenges our understanding of reality itself! #21DaysChallenge #QuantumComputing #QuantumMechanics #EPRParadox #BellsInequality #PhysicsLearning #QuCode