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A particle in the harmonic oscillator potential starts out in the state ψ(x,0)=A[3ψ₀(x)+4ψ₁(x)].

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Harmonic Oscillator ⟨x⟩, ⟨p⟩, ⟨x²⟩ ⟨p²⟩ ⟨T⟩ Ladder operator method

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Harmonic Oscillator ⟨x⟩, ⟨p⟩, ⟨x²⟩ ⟨p²⟩

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construct wavefunction for harmonic oscillator for n=1,2

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Infinite square well potential with constant initial wavefunction A

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Infinite Square Well, potentially, the initial wave function = Ax , A(a-x)

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Infinite square well—wavefunction-mixture of two stationary states. Normalise, exp value of x,p

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Infinite square well expectation value of x, x², p, p², uncertainty in position and momentum

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Normalize wavefunction A(a²-x²) find the expectation value of x, x², p, p², sigma x and sigma p

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Integration of the probability current with different wavefunctions and the same potential

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probability current

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Normalization Aexp(-α(mx²ħ)+it) and expectation value x, x², p, p² sigma of position and momentum

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Ehrenfest theorem momentum and position, momentum and force

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normalize wavefunction, expectation value of x and x^2

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Expectation value of x and normalize the given function

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Einstein B coefficient from n=2; l=1; m=0 to n=1; l=0; m=0 state

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Temperature for the transition probability for spontaneous emission is equal to stimulated emission

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Einstein A coefficient state 310 to state 200

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Angular momentum raising operator to find spherical harmonics for l=m=l and normalize it

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Angular momentum Raising operator Spherical Harmonics for l=2=m from l=2;m=1

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Angular momentum operator spherical polar coordinates - A simple way

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Angular momentum operator spherical polar coordinates

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Raising and lowering operator angular momentum - determination of constant

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Linear combination of wavefunction n=2,l=1,m=1 and -1; expectation value of potential energy V

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Expectation value of x^2 in the state n=2, l=1, m=1 state - hydrogen atom

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Expectation values of r and r^2 for the hydrogen atom in the ground state in terms of Bohr Radius

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Derivation of spherical harmonics Ylm for l=0,1,2; wave function construction

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Normalize Radial part of wavefunction R20, R21 and construct wavefunction for nlm=200,211,210,21-1

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diatomic molecule harmonic oscillator reduced mass unknown atom vibrational frequency

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Classes in group theory ammonia molecule C3v point group

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