# Long pages

### From Substepr

Showing below up to **50** results starting with #**1**.

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- (hist) Use COMSOL Multiphysics to make a 2D simulation of Poiseuille flow [10,188 bytes]
- (hist) Define objectivism [8,349 bytes]
- (hist) Quantise the coupled harmonic oscillator [8,276 bytes]
- (hist) Quantum field theory [5,396 bytes]
- (hist) The structure of Substepr [5,052 bytes]
- (hist) Show that the scalar (or inner) product of position \(x\) and momentum \(p\) can be written as an exponential in terms of \(x\) and \(p\) [4,889 bytes]
- (hist) Use the Bogoliubov transformation to diagonalise the BCS superconductivity Hamiltonian [4,824 bytes]
- (hist) Derive the quantised Hamiltonian corresponding to the Dirac equation [4,637 bytes]
- (hist) Create a new page in Substepr [4,390 bytes]
- (hist) Use the Trachtenberg speed system of basic mathematics to multiply 6250188 by 6 [4,385 bytes]
- (hist) Find the probability of a player being given exactly one ace in a Bridge deal [4,325 bytes]
- (hist) Use the mean field approximation to simplify the BCS superconductivity Hamiltonian [3,901 bytes]
- (hist) Build the open source car suggested on www.theoscarproject.org [3,848 bytes]
- (hist) Build an all-electric car [3,823 bytes]
- (hist) Other points [3,805 bytes]
- (hist) Find a fossil [3,787 bytes]
- (hist) Show that the Hamiltonian of the quantum elastic chain can be represented as a sum of harmonic oscillator Hamiltonians [3,638 bytes]
- (hist) Use the Trachtenberg speed system of basic mathematics to multiply 443052 by 6 [3,464 bytes]
- (hist) Plan the construction of a modern-day pyramid as an open project hosted by Substepr [3,320 bytes]
- (hist) Derive the quantised Hamiltonian corresponding to the charged Klein-Gordon equation [3,295 bytes]
- (hist) Show that the bosonic commutation relations of the creation and annihilation operators are preserved by the Bogoliubov transformation [3,278 bytes]
- (hist) Use the Euler-Lagrange equation [3,257 bytes]
- (hist) Donor name or URL submission instructions [3,202 bytes]
- (hist) Calculate expectation values for \(x^4\) in state \(n\) using ladder operators [3,183 bytes]
- (hist) Find the fraction of bosons not in the concentrate in a weakly interacting bosonic superfluid [3,161 bytes]
- (hist) Show that if the raising operator acts on an eigenstate of the number operator, the result is also an eigenstate of the number operator [3,114 bytes]
- (hist) Represent an arbitrary number state \(n\) in terms of creation operators and the vacuum state [3,044 bytes]
- (hist) Derive the quantised Hamiltonian corresponding to the uncharged Klein-Gordon equation [2,997 bytes]
- (hist) Find the excitation spectrum for a weakly interacting bosonic superfluid [2,862 bytes]
- (hist) Main Page [2,767 bytes]
- (hist) Derive the equations of motion for arbitrarily many coupled harmonic oscillators with alternating masses [2,719 bytes]
- (hist) Make a ring around a planet that can shrink or expand instead of using a space elevator [2,707 bytes]
- (hist) Prove and demonstrate the existence of ladder operators for the simple harmonic oscillator [2,676 bytes]
- (hist) Show that if the lowering operator acts on a non-zero eigenstate of the number operator, the result is also an eigenstate of the number operator [2,653 bytes]
- (hist) Use the Trachtenberg speed system of basic mathematics to multiply 8234 by 6 [2,638 bytes]
- (hist) Top donors [2,531 bytes]
- (hist) Create something profound [2,494 bytes]
- (hist) Use the Trachtenberg speed system to multiply 98834 by 11 [2,425 bytes]
- (hist) Prove that the lowering operator lowers the state of the simple harmonic oscillator [2,399 bytes]
- (hist) Use the Trachtenberg speed system to multiply 63247 by 12 [2,385 bytes]
- (hist) Act on the Hamiltonian \(H=F(a^\dagger a+b^\dagger b)+G(a^\dagger b^\dagger+ab)\) with the Bogoliubov transformation [2,361 bytes]
- (hist) Show that number states are eigenstates of the Hamiltonian operator for a simple harmonic oscillator [2,322 bytes]
- (hist) Integrate using 'Integration by parts' [2,296 bytes]
- (hist) Show that the scalar (or inner) product of basis state \(x\) and quantum state \(\phi\) with the momentum operator \(p\) can be written as a derivative [2,278 bytes]
- (hist) Show that the scalar (or inner) product of basis state \(p\) and quantum state \(\phi\) with the position operator \(x\) can be written as a derivative [2,272 bytes]
- (hist) Find the quadratic bosonic theory that describes a 1-dimensional Heisenberg ferromagnet [2,235 bytes]
- (hist) Find the eigenstate of the total spin operator in the Schwinger boson representation [2,149 bytes]
- (hist) Find the distribution of the number of observations until the value of the first observation is exceeded. [2,128 bytes]
- (hist) Find the gap energy \(\Delta\) of the BCS superconductor [2,125 bytes]
- (hist) Find the Hamiltonian for the interaction between phonons and optical phonons [2,124 bytes]