Undergraduate quantum mechanics: lost opportunities for engaging motivated students?

Abstract

Undergraduate quantum mechanics: lost opportunities for engaging motivated students?.

Student perceptions of math-physics interactions throughout spins-first quantum mechanics

“…While Johansson [7] found that students would either have to accept the difficulty of the mathematics or become alienated by quantum mechanics, these results suggest that the SF paradigm may allow students to enter quantum mechanics without immediately experiencing difficulty with the mathematics. Ongoing work seeks to address these questions further in both SF and PF classrooms in order to make a direct comparison of student perceptions of the mathematics and physics content within the two paradigms.…”

“…In this approach, students are simultaneously introduced to the new ideas of quantum mechanics and a high level of mathematical rigor. Sadaghiani [1] argues that this approach gives more emphasis to mathematical skill solving complex integrals and differential equations than to the postulates of quantum mechanics.. Further, Johansson found that students in a PF course, either accepted having to learn quantum mechanics in this mathematical way or would experience "crisis" leading to the student distancing themselves from the subject of physics [7]. This paper presents the results of a preliminary survey given to students at different points in a SF course to identify if there were any differences in students' perspectives of the relationship between math and physics when they studied discrete spin systems and continuous wave functions of position.…”

Improving student understanding of corrections to the energy spectrum of the hydrogen atom for the Zeeman effect

“…diagonalize the entire eight-dimensionalĤ 0 matrix instead of diagonalizing the two separate 2 × 2 submatrices of the block diagonal matrixĤ 0 =Ĥ 0 fs +Ĥ 0 Z When asked to determine the first order corrections to the energies for the intermediate field Zeeman effect for the n ¼ 2 degenerate subspace ofĤ 0 , some students correctly identified that one can initially choose either a basis consisting of states in the coupled representation or a basis consisting of states in the uncoupled representation and then diagonalizeĤ 0 ¼Ĥ 0 fs þĤ 0 Z in each degenerate subspace ofĤ 0 . For example, in a basis consisting of states in the coupled representation (jn; l; jm j i), the perturbation matrixĤ 0 ¼Ĥ 0 Z þĤ 0 fs corresponding to the n ¼ 2 subspace is given below [in which γ ¼ ðα=8Þ 2 13.6 eV, α ¼ e 2 =4πϵ 0 ℏc, β ¼ μ B B ext , and the basis states are chosen in the order j2; 0; 1 2 ; 1 2 i, j2; 0; 1 2 ; − 1 2 i, j2; 1; 3 2 ; 3 2 i, j2; 1; 3 2 ; − 3 2 i, j2; 1; 3 2 ; 1 2 i, j2; 1; 1 2 ; 1 2 i, j2; 1; 3 2 ; − 1 2 i, and j2; 1; 1 2 ; − 1 2 i]: However, when finding the corrections to the energy spectrum, some students attempted to diagonalize the entire 8 × 8Ĥ 0 matrix in the n ¼ 2 degenerate subspace ofĤ 0 . While this approach is correct, it is easier to diagonalize the 8 × 8Ĥ 0 matrix by diagonalizingĤ 0 only in the block diagonal subspaces with smaller dimensions than the initial 8 × 8Ĥ 0 matrix, i.e., the two separate 2 × 2 matrices…”

“…Student 2: We must make an effort to diagonalizeĤ 0 only in those block diagonal subspaces with smaller dimensions in order to diagonalize the entireĤ 0 matrix in the degenerate subspace ofĤ 0 to obtain the good basis set. When I calculate theĤ 0 matrix for n ¼ 2 in the coupled representation and the angular basis states are chosen in the order jψ 1 i ¼ j2; 0; 1 2 ; 1 2 i, jψ 2 i ¼ j2; 0; 1 2 ; − 1 2 i, jψ 3 i ¼ j2; 1; 3 2 ; 3 2 i, jψ 4 i ¼ j2; 1; 3 2 ; − 3 2 i, jψ 5 i ¼ j2; 1; 3 2 ; 1 2 i, jψ 6 i¼j2;1; 1 2 ; 1 2 i, jψ 7 i ¼ j2; 1; 3 2 ; − 1 2 i, and jψ 8 i ¼ j2; 1; 1 2 ; − 1 2 i, I get the block diagonal matrix H 0 beloŵ We will only need to diagonalize the 2 × 2 matrices…”

Analysis of secondary school quantum physics curricula of 15 different countries: Different perspectives on a challenging topic

“…And finally, popular science topics like quantum teleportation, parallel worlds, or quantum computers appeal to the imagination. Similar to Einstein's theory of relativity, QP fascinates scientists as well as students [4][5][6][7], and educators should not miss the chance to give physics a more attractive image.…”