{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

ConceptTests_part2_all

ConceptTests_part2_all - Quantum I(PHYS 3220 concept...

Info icon This preview shows pages 1–15. Sign up to view the full content.

View Full Document Right Arrow Icon
Quantum I (PHYS 3220) concept questions
Image of page 1

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Schrödinger Equation
Image of page 2
Consider the eigenvalue equation How many of the following give an eigenfunction and corresponding eigenvalue? I. f(x) = sin(kx), C = +k 2 II. f(x) = exp(-x), C = +1 III. f(x) = exp(i k x), C = -k 2 IV. f(x) = x 3 , C = 6 A) 1 B) 2 C) 3 D) all 4 E) None ) ( )] ( [ 2 2 x f C x f dx d = 31
Image of page 3

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Is ? d dt Ψ * ( x , t ) -∞ Ψ ( x , t ) dx = d dt Ψ * ( x , t ) Ψ ( x , t ) ( 29 -∞ dx A)Yes, no problem! B)There’s something not right about this…
Image of page 4
Two particles, 1 and 2, are described by plane wave of the form exp[i(kx–ωt)]. Particle 1 has a smaller wavelength than particle 2: λ 1 < λ 2 Which particle has larger momentum? A) particle 1 B) particle 2 C) They have the same momentum D) It is impossible to answer based on the info given. 36
Image of page 5

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Ψ 1 (x, t) and Ψ 2 (x, t) are two solutions of the time-dependent SE. Is Ψ sum (x, t) = a Ψ 1 (x, t) + b Ψ 1 (x, t) also a solution of the TDSE? A) Yes, always B) No, never C) Depends on Ψ 1 (x, t) and Ψ 2 (x, t) D) Depends on a and b 32
Image of page 6
Ψ 1 (x, t) and Ψ 2 (x, t) are two NORMALIZED solutions of the time- dependent SE. Is Ψ sum (x, t) = a Ψ 1 (x, t) + b Ψ 1 (x, t) also a normalized solution of the TDSE? A) Yes, always B) No, never C) Depends on Ψ 1 (x, t) and Ψ 2 (x, t) D) Depends on a and b 32
Image of page 7

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Which expression below would be the QM equation for <KE>? A) B) C) D) None of these! E) More than one! ( 29 x t x t x m k d ) , ( ) , ( 2 * 2 2 - Ψ Ψ - ( 29 x t x x t x m d ) , ( ) , ( 2 2 2 * 2 - Ψ Ψ - ( 29 x t x t x x m d ) , ( ) , ( 2 * 2 2 2 - Ψ Ψ -
Image of page 8
After assuming a product form solution Ψ (x,t) = ψ (x)· φ (t), the TDSE becomes If the potential energy function V in the Schrödinger Equation is a function of time, as well as x [V = V(x,t)] would separation of variables still work; that is, would there still be solutions to the SE of the form Ψ (x,t) = ψ (x)· φ (t)? A) Yes, always B) No, never C) Depends on the functional dependence of V on x and t E V x m t i = + - = 2 2 2 1 2 1 ψ ψ ∂ϕ ϕ 30
Image of page 9

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Ψ 1 (x, t) and Ψ 2 (x, t) are two solutions of the time-dependent SE. Is Ψ sum (x, t) = a· Ψ 1 (x, t) + b· Ψ 2 (x, t) also a solution of the TDSE? A) Yes B) No C) Depends on Ψ 1 (x, t) and Ψ 2 (x, t) D) Depends on a and b 32
Image of page 10
Do you know what the momentum operator is? A) Yes B) No 33
Image of page 11

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Do you plan to attend today’s Tutorial (on relating classical to Quantum, and qualitative “sketching” of wave functions) A) Yes, at 3 pm B) Yes, at 4 pm C) Perhaps, more likely at 3 D) Perhaps, more likely at 4 E) No, can’t come/not planning on it.
Image of page 12
Given Ψ n (x, t) as one of the eigenstates of Ĥ Ψ n = E n Ψ n , what is the expectation value of the Hamiltonian-squared? A) E n B) E n 2 C) zero D) E n 2 – E n E) Something else/it really depends!! ? d ) H ˆ ( H ˆ ˆ * 2 = Ψ Ψ = x H n n 34
Image of page 13

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Ψ 1 and Ψ 2 are two energy eigenstates of the Hamiltonian operator. They are non-degenerate, meaning they have different eigenvalues E 1 and E 2 .
Image of page 14
Image of page 15
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern