Question

A particle is trapped in a one-dimensional potential energy well given by: 100 x < 0 0 < x <L U(x) = L < x < 2L (20. x > 2L Consider the case when U, < E < 20., where E is the particle energy. a. Write down the solutions to the time-independent Schrödinger equation for the wavefunction in the four regions using appropriate coefficients. Define any parameters used in terms of the particles mass m, E, U., and ħ. Do not solve for the coefficients or normalize your wavefunctions, simply write the form of the solutions. [2]

A particle is trapped in a one-dimensional potential energy well given by: 100 x < 0 0 < x <L U(x) = L < x < 2L (20. x > 2L Consider the case when U, < E < 20., where E is the particle energy. a. Write down the solutions to the time-independent Schrödinger equation for the wavefunction in the four regions using appropriate coefficients. Define any parameters used in terms of the particles mass m, E, U., and ħ. Do not solve for the coefficients or normalize your wavefunctions, simply write the form of the solutions. [2]

Answer 1

. (M) = ww Luo osas L alsk sal Que nal Foy I- Regio (Particle com not exist in intine E< QU For Region - - Det (U=U. U + UoY's = EU am dna Evo drea - amuola = -2mEva dne t

de dm (E - Us) 47 zo m2 + k} R =D K = vam cevo) m = Iiki to = A plkn + Beinat For region cv=O) = Eva am duz d2d in tamE Yo =0 d²4. + K² Via = K2=VQME Ka to = cel kau berikut region in Exavo) - 2 days + PUOYA EVO am duz d²lv + amCE -20o) y,u =0 du? 2 diu - am (QU. -E) tu to anz

___ d2diu - K2 Yv.co dur 40-E) र = ० +k m SH = Epkit + Fe-K34