🌊 CollapsedWave
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Last 10 notes on 🌊 CollapsedWaveQuartz -- quartz.jzhao.xyzThe Schrodinger and Heisenberg pictures are equivalent
https://collapsedwave.com/Physics/Quantum/Results/The-Schrodinger-and-Heisenberg-pictures-are-equivalent
https://collapsedwave.com/Physics/Quantum/Results/The-Schrodinger-and-Heisenberg-pictures-are-equivalentThe Schrodinger picture and Heisenberg picture are equivalent, in the sense that we obtain the same results from either. Results are observed through Measurement, so this result means that Measurements are consistent across pictures Proof In the Heisenberg picture, we consider the Quantum state ψ fixed and the Quantum observable A(t) evolves in time.Fri, 13 Sep 2024 15:25:43 GMTThere is no measurement uncertainty iff the eigenstate is in the kernel of the operator
https://collapsedwave.com/Physics/Quantum/Results/There-is-no-measurement-uncertainty-iff-the-eigenstate-is-in-the-kernel-of-the-operator
https://collapsedwave.com/Physics/Quantum/Results/There-is-no-measurement-uncertainty-iff-the-eigenstate-is-in-the-kernel-of-the-operatori.e. ΔψA=0⇔Aψ=0, where A is an Operator ψ is a Quantum state. ΔψA is the Measurement uncertainty Proof ⇐ is trivial. To prove ⇒, we first define B:=A−⟨A⟩ψ, where ⟨⋅⟩ψ is the Expectation operator, so that ⟨B⟩ψ=0 ΔψB=ΔψA 0=ΔψB=⟨B2⟩ψ=⟨ψ,B2ψ⟩=⟨Bψ,Bψ⟩=∥Bψ∥.Fri, 13 Sep 2024 15:25:43 GMTTime-independent Schrodinger equation derivation
https://collapsedwave.com/Physics/Quantum/Results/Time-independent-Schrodinger-equation-derivation
https://collapsedwave.com/Physics/Quantum/Results/Time-independent-Schrodinger-equation-derivationWe can derive the Time-independent Schrodinger equation via Separation of variables as follows: iℏ∂t∂∣ψt⟩iℏ∂t∂ψ0(x)T(t)iℏψ0(x)T′(t)iℏT(t)T′(t)=H∣ψt)⟩=Hψ0(x)T(t)=T(t)Hψ0(x)=ψ0(x)Hψ0(x)plugging ...Fri, 13 Sep 2024 15:25:43 GMTQuantum Harmonic Oscillator
https://collapsedwave.com/Physics/Quantum/Systems/Quantum-Harmonic-Oscillator
https://collapsedwave.com/Physics/Quantum/Systems/Quantum-Harmonic-OscillatorSystem described by the Hamiltonian H=∑i=0n2mPi+21mωiXi2.Fri, 13 Sep 2024 15:25:43 GMTBohr radius
https://collapsedwave.com/Physics/Units/Bohr-radius
https://collapsedwave.com/Physics/Units/Bohr-radiusα0=e2me4πϵ0ℏ2=mecαℏ≈5.2E(−11)m , where ϵ0 is the vacuum permittivity. ℏ is the reduced planck constant me is the mass of an electron e is the elementary charge c is the speed of light α is the fine-structure constant The Bohr radius is the most likely distance between the nucleus and the electron in the hydrogen atom when it is in a Ground state.Fri, 13 Sep 2024 15:25:43 GMTNewton
https://collapsedwave.com/Physics/Units/Newton
https://collapsedwave.com/Physics/Units/NewtonNewton is the SI Unit of Force.Fri, 13 Sep 2024 15:25:43 GMTPlanck's reduced constant
https://collapsedwave.com/Physics/Units/Planck's-reduced-constant
https://collapsedwave.com/Physics/Units/Planck's-reduced-constantℏ:=2πh, where h is planck’s constant. This is useful as many algebraic manipulations simplify by including the 2π term in planck’s constant.Fri, 13 Sep 2024 15:25:43 GMTSI Unit
https://collapsedwave.com/Physics/Units/SI-Unit
https://collapsedwave.com/Physics/Units/SI-UnitBase units, from which all other units can be derived: seconds for Time meters for lengths kilograms for mass amperes for electric current kelvin for temperature mole for amount of ...Fri, 13 Sep 2024 15:25:43 GMTApplying Machine Learning to Fraud Detection @ Farfetch
https://collapsedwave.com/Whimsical/Applying-Machine-Learning-to-Fraud-Detection-@-Farfetch
https://collapsedwave.com/Whimsical/Applying-Machine-Learning-to-Fraud-Detection-@-FarfetchSupervisor: Cristina Cerqueira When I first joined Farfetch I was told they were looking for someone to implement Machine Learning algorithms to help predict possible fraud attempts ...Fri, 13 Sep 2024 15:25:43 GMTBabble
https://collapsedwave.com/Whimsical/Babble
https://collapsedwave.com/Whimsical/BabbleThe generation of ideas without any filters. It is nicely described in this post from LessWrong.Fri, 13 Sep 2024 15:25:43 GMT