Problem library

Find a problem

Search by course or topic.

Search problems

Area

AllMathPhysics

SubjectCourseTopic

Topic choices for Quantum Mechanics I are shortened. Search still covers every problem.

More filters

StatusSkillProblem styleFind a private labelPrivate labelFavorites

Clear

Browsing still works.Sign in to use progress, saved problems and private labels. Problem search and previews remain available.

Progress labels

IndependentSolved with helpIncorrect / unresolvedDraft in progressNot attemptedReview due

Problem results

ProblemsBuild a practice set

QM:010117A qutrit Born audit of A: eigenvalues (−a, 0, 2a) and collapse of the zero outcome to |2⟩

Quantum Mechanics Qutrit Born RuleQuantum Mechanics Observable Moments Collapse

States, observables, measurement, and time evolutionQuantum Mechanics I · Mixed review

QM:010118Postselect the plane spanned by u and v, then name the normalized complement

View access options

Quantum Mechanics Subspace ProjectorQuantum Mechanics Postselection Complement

States, observables, measurement, and time evolutionQuantum Mechanics I · Mixed review

QM:010219Two stationary states of the infinite well: energy moments, a midpoint density, and the 3E₁ clock

View access options

Quantum Mechanics Infinite Well SuperpositionQuantum Mechanics Interference Density Recurrence

One-dimensional bound and scattering problemsQuantum Mechanics I · Mixed review

QM:010220One bound state of −α δ(x): the derivative jump, the exponential tails, and ⟨|x|⟩

View access options

Quantum Mechanics Delta Bound StateQuantum Mechanics Derivative Jump Tails

One-dimensional bound and scattering problemsQuantum Mechanics I · Mixed review

QM:010221Rectangular-barrier matching at E=V₀/2 with κa=ln 3 yields T=9/25, not the opaque exponential

View access options

Quantum Mechanics Rectangular Barrier MatchingQuantum Mechanics Exact Versus Opaque Transmission

One-dimensional bound and scattering problemsQuantum Mechanics I · Mixed review

QM:010322The oscillator state (|0>+i|1>)/sqrt(2) has <x>(t)=x0 sin(omega t) and Delta x Delta p=hbar/sqrt(2) at t=0

View access options

Quantum Mechanics Oscillator Heisenberg MeansQuantum Mechanics Oscillator Variance Product

Operators, commutators, and symmetriesQuantum Mechanics I · Mixed review

QM:010323The ring state (|2>+i|-2>)/sqrt(2) has certain energy 2 hbar^2/I and density [1+sin(4 phi)]/(2 pi)

View access options

Quantum Mechanics Ring Reflection DegeneracyQuantum Mechanics Ring Azimuthal Density

Operators, commutators, and symmetriesQuantum Mechanics I · Mixed review

QM:010424A +x spin measured along n=(3/5,0,4/5) has P+=4/5, then P(z+|n+)=9/10

View access options

Quantum Mechanics Spin Direction BornQuantum Mechanics Sequential Spin Projection

Angular momentum and spinQuantum Mechanics I · Mixed review

QM:010425The superposition sqrt(2/5) Y_2^1 + i sqrt(3/5) Y_3^{-2} has <L^2>=48 hbar^2/5 and Delta Lz=3 sqrt(6) hbar/5

View access options

Quantum Mechanics Spherical Harmonic L2 SpectrumQuantum Mechanics LZ Variance Conditional

Angular momentum and spinQuantum Mechanics I · Mixed review

QM:010526The hydrogen 1s radial density has mode a0, <r>=3 a0/2, and tail 5 e^{-2} beyond a0

View access options

Quantum Mechanics Hydrogen 1S Radial DensityQuantum Mechanics Hydrogen 1S Moments Cdf

Central potentials and hydrogenic structureQuantum Mechanics I · Mixed review

QM:010527Kepler Veff has circular r0=L^2/(mk), Vmin=-mk^2/(2L^2), and small-oscillation omega=mk^2/[hbar^3(l(l+1))^(3/2)]

View access options

Quantum Mechanics 1 Kepler Effective Potential Circular OrbitQuantum Mechanics 1 Radial Small Oscillation Frequency

Central potentials and hydrogenic structureQuantum Mechanics I · Mixed review

QM:010528Hydrogen 2p radial density r^4 e^{-r/a0}/(24 a0^5) has mode 4a0, <r>=5a0, Delta=sqrt(5) a0, and P(r<2a0)=1-7e^{-2}

View access options

Quantum Mechanics 1 Hydrogen Radial Density MomentsQuantum Mechanics 1 Spherical Harmonic Polar Cone

Central potentials and hydrogenic structureQuantum Mechanics I · Mixed review

QM:010629The mixture (3/4)|0><0|+(1/4)|+><+| is [[7/8,1/8],[1/8,1/8]] with Bloch (1/4,0,3/4) and purity 13/16

View access options

Quantum Mechanics 1 Qubit Mixture Bloch VectorQuantum Mechanics 1 Purity Spectrum Basis Probabilities

Tensor products and composite systemsQuantum Mechanics I · Mixed review

QM:010630Exchange H=J(|01><10|+|10><01|) sends |01> to cos(theta)|01>-i sin(theta)|10> with concurrence |sin 2 theta|

View access options

Quantum Mechanics 1 Exchange Two Qubit EvolutionQuantum Mechanics 1 Concurrence And Swap Time

Tensor products and composite systemsQuantum Mechanics I · Mixed review

QM:010631The p=1/2 Werner state has fidelity 5/8, negativity 1/8, and CHSHmax=sqrt(2) with no Bell violation

View access options

Quantum Mechanics 1 Werner Partial Transpose NegativityQuantum Mechanics 1 Isotropic Chsh Bound

Tensor products and composite systemsQuantum Mechanics I · Mixed review

Showing 15 of 15 matching problems.

Find a problem

Loading the problem library…

Find a problem

Problem results

QM:010117A qutrit Born audit of A: eigenvalues (−a, 0, 2a) and collapse of the zero outcome to |2⟩

QM:010118Postselect the plane spanned by u and v, then name the normalized complement

QM:010219Two stationary states of the infinite well: energy moments, a midpoint density, and the 3E₁ clock

QM:010220One bound state of −α δ(x): the derivative jump, the exponential tails, and ⟨|x|⟩

QM:010221Rectangular-barrier matching at E=V₀/2 with κa=ln 3 yields T=9/25, not the opaque exponential

QM:010322The oscillator state (|0>+i|1>)/sqrt(2) has <x>(t)=x0 sin(omega t) and Delta x Delta p=hbar/sqrt(2) at t=0

QM:010323The ring state (|2>+i|-2>)/sqrt(2) has certain energy 2 hbar^2/I and density [1+sin(4 phi)]/(2 pi)

QM:010424A +x spin measured along n=(3/5,0,4/5) has P+=4/5, then P(z+|n+)=9/10

QM:010425The superposition sqrt(2/5) Y_2^1 + i sqrt(3/5) Y_3^{-2} has <L^2>=48 hbar^2/5 and Delta Lz=3 sqrt(6) hbar/5

QM:010526The hydrogen 1s radial density has mode a0, <r>=3 a0/2, and tail 5 e^{-2} beyond a0

QM:010527Kepler Veff has circular r0=L^2/(mk), Vmin=-mk^2/(2L^2), and small-oscillation omega=mk^2/[hbar^3(l(l+1))^(3/2)]

QM:010528Hydrogen 2p radial density r^4 e^{-r/a0}/(24 a0^5) has mode 4a0, <r>=5a0, Delta=sqrt(5) a0, and P(r<2a0)=1-7e^{-2}

QM:010629The mixture (3/4)|0><0|+(1/4)|+><+| is [[7/8,1/8],[1/8,1/8]] with Bloch (1/4,0,3/4) and purity 13/16

QM:010630Exchange H=J(|01><10|+|10><01|) sends |01> to cos(theta)|01>-i sin(theta)|10> with concurrence |sin 2 theta|

QM:010631The p=1/2 Werner state has fidelity 5/8, negativity 1/8, and CHSHmax=sqrt(2) with no Bell violation

Edit private labels

Find a problem

Find a problem

Problem results

QM:010117A qutrit Born audit of A: eigenvalues (−a, 0, 2a) and collapse of the zero outcome to |2⟩

QM:010118Postselect the plane spanned by u and v, then name the normalized complement

QM:010219Two stationary states of the infinite well: energy moments, a midpoint density, and the 3E₁ clock

QM:010220One bound state of −α δ(x): the derivative jump, the exponential tails, and ⟨|x|⟩

QM:010221Rectangular-barrier matching at E=V₀/2 with κa=ln 3 yields T=9/25, not the opaque exponential

QM:010322The oscillator state (|0>+i|1>)/sqrt(2) has <x>(t)=x0 sin(omega t) and Delta x Delta p=hbar/sqrt(2) at t=0

QM:010323The ring state (|2>+i|-2>)/sqrt(2) has certain energy 2 hbar^2/I and density [1+sin(4 phi)]/(2 pi)

QM:010424A +x spin measured along n=(3/5,0,4/5) has P+=4/5, then P(z+|n+)=9/10

QM:010425The superposition sqrt(2/5) Y_2^1 + i sqrt(3/5) Y_3^{-2} has <L^2>=48 hbar^2/5 and Delta Lz=3 sqrt(6) hbar/5

QM:010526The hydrogen 1s radial density has mode a0, <r>=3 a0/2, and tail 5 e^{-2} beyond a0

QM:010527Kepler Veff has circular r0=L^2/(mk), Vmin=-mk^2/(2L^2), and small-oscillation omega=mk^2/[hbar^3(l(l+1))^(3/2)]

QM:010528Hydrogen 2p radial density r^4 e^{-r/a0}/(24 a0^5) has mode 4a0, <r>=5a0, Delta=sqrt(5) a0, and P(r<2a0)=1-7e^{-2}

QM:010629The mixture (3/4)|0><0|+(1/4)|+><+| is [[7/8,1/8],[1/8,1/8]] with Bloch (1/4,0,3/4) and purity 13/16

QM:010630Exchange H=J(|01><10|+|10><01|) sends |01> to cos(theta)|01>-i sin(theta)|10> with concurrence |sin 2 theta|

QM:010631The p=1/2 Werner state has fidelity 5/8, negativity 1/8, and CHSHmax=sqrt(2) with no Bell violation

Edit private labels

Problem results

QM:010117A qutrit Born audit of A: eigenvalues (−a, 0, 2a) and collapse of the zero outcome to |2⟩View problem statement

Find a problem

Problem results

QM:010117A qutrit Born audit of A: eigenvalues (−a, 0, 2a) and collapse of the zero outcome to |2⟩View problem statement

QM:010117A qutrit Born audit of A: eigenvalues (−a, 0, 2a) and collapse of the zero outcome to |2⟩

QM:010117A qutrit Born audit of A: eigenvalues (−a, 0, 2a) and collapse of the zero outcome to |2⟩